E1 (6263274) 1. Question Details SCalc7 0.Diagnostic ...rfrith.uaa.alaska.edu/Calculus/ESolns/E1_Solns_Fall2014.pdf · x 2b x 1 6a − 2b True False 2. Question Details SCalc7 0.Diagnostic.Algebra.002b

9/9/2014 Assignment Previewer

http://www.webassign.net/v4cgi/assignments/preview.tpl?aid=6263274&deployment=9952063&UserPass=e02be4870d7dad87aee99d87d1bc5f65 1/53

Question 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455

E1 (6263274)

Due: Mon Sep 8 2014 10:00 PM AKDT

1. -Question Details SCalc7 0.Diagnostic.Algebra. [2743008]

1) Evaluate each expression without using a calculator.

2) Simplify each expression. Write your answer without negative exponents.

3) Expand and simplify.

4) Factor each expression.

(a) (−3)4 = 81

(b) −34 = -81

(c) 3(−4) = 1/81

(d) = 36624

622

(e) = 16/934

−2

(f) 16−3/4 = 1/8

(a) − = 192 108

(b) (4a3b3)(4ab2)2 =

(c) = 4x3/2y3

x2y−1/2

−2

(a) 2(x + 4) + 6(2x − 6) =

(b) (x + 2)(5x − 4) =

(c) ( + )( − ) = 7a 2b 7a 2b

(d) (2x + 4)2 =

(e) (x + 5)3 =

(a) 36x2 − 49 =

(b) 2x2 + 4x − 6 =



5) Simplify the rational expression.

6) Rationalize the denominator of (a) and the numerator of (b) and simplify.

7) Rewrite by completing the square.

8) Solve the equation. (Find only the real solutions. Enter your answers as a comma-separated list.)

x =

(c) x3 − 4x2 − 4x + 16 =

(d) x4 + 27x =

(e) 3x3/2 − 9x1/2 + 6x−1/2 =

(f) x3y − 25xy =

(a) = x2 + 3x + 2x2 − x − 2

(b) · = 2x2 − x − 1x2 − 9

x + 32x + 1

(c) − = x2

x2 − 64x + 4x + 8

(d) = −

−

yx

xy

3y

3x

(a) = − 3

13

10

(b) = − 6h

36 + h

(a) x2 + x + 3 =

(b) 2x2 − 16x + 25 =

(a) x + 4 = 10 − x2

(b) = 3xx + 2

3x − 2x

x =

(c) x2 − x − 6 = 0



9) Solve each inequality. Write your answer using interval notation.

10) State whether each equation is true or false.

x =

(d) 3x2 + 4x + 1 = 0

x =

(e) x4 − 3x2 + 2 = 0

x =

(f) 3|x − 5| = 8

x =

(g) 2x(4 − x)−1/2 − 3 = 04 − x

x =

(a) −5 < 5 − 2x ≤ 7

(b) x2 < 2x + 24

(c) x(x − 2)(x + 4) > 0

(d) |x − 7| < 4

(e) ≤ 12x − 6x + 1

(a) (4p + 5q)2 = 16p2 + 25q2

True

False

(b) = , for a, b > 0ab a b

True

False

(c) = 4a + 6b16a2 + 36b2



If you have had difficulty with these problems, you may wish to consult the Review of Algebra on the websiteStewartCalculus.com.

True

False

(d) = 6 + T, for C ≠ 06 + TCC

True

False

(e) = − , for x, y ≠ 0 and x ≠ y13x − 8y

13x

18y

True

False

(f) = , for a, b, x ≠ 0 and 6a ≠ 2b −

1x

6ax

2bx

16a − 2b

True

False

2. -Question Details SCalc7 0.Diagnostic.Algebra.002b. [2742892]

Simplify the expression. Write your answer without negative exponents.

If you have had difficulty with this problem, you may wish to consult the Review of Algebra on the websiteStewartCalculus.com.

(3a2b3)(5a4b4)2

3. -Question Details SCalc7 0.Diagnostic.Algebra.002c. [2742597]

Simplify the expression. Write your answer without negative exponents.


5x7/2y5

x6y−3/2

−2




Expand and simplify.


+ − f a f a

5. -Question Details SCalc7 0.Diagnostic.Algebra.003e. [2742836]

Expand and simplify.


(x + 3)3


Factor the expression.


2x2 + 7x − 30




x3 − 2x2 − 16x + 32




4x3/2 − 12x1/2 + 8x−1/2



9. -Question Details SCalc7 0.Diagnostic.Algebra.005a. [2742859]

Simplify the rational expression.


x2 + 9x + 8x2 − 7x − 8




− x2

x2 − 64x + 4x + 8




· 4x2 − 3x − 1x2 − 49

x + 74x + 1

12. -Question Details SCalc7 0.Diagnostic.Algebra.005d. [2742783]



−

−

yx

xy

3y

3x




Rationalize the numerator and simplify.


− 4h

16 + h


Rewrite by completing the square.


2x2 − 4x + 13


Solve the equation. (Find only the real solutions. Enter your answers as a comma-separated list.)

x =


= 2xx + 2

2x − 2x

16. -Question Details SCalc7 0.Diagnostic.Algebra.008f. [2742817]


x =


7|x − 2| = 10



17. -Question Details SCalc7 0.Diagnostic.Algebra.008g. [2743030]


x =


4x(5 − x)−1/2 − 3 = 05 − x


Solve the inequality. Write your answer using interval notation.


x2 < 4x + 12




x(x − 2)(x + 7) > 0




≤ 12x − 9x + 1




State whether the equation is true or false.


= 4a + 4b16a2 + 16b2

True

False

22. -Question Details SCalc7 0.Diagnostic.Algebra.010f. [2742497]

State whether the equation is true or false.


= , for a, b, x ≠ 0 and 4a ≠ 8b −

1x

4ax

8bx

14a − 8b

True

False

23. -Question Details SCalc7 0.Diagnostic.AnalyticGeometry. [2743037]

1) Find an equation for the line that passes through the point where the following is true.

(a) has slope

(b) is parallel to the x-axis

(c) is parallel to the y-axis

(d) is parallel to the line

2) Find an equation for the circle that has center and passes through the point

3) Find the center and radius of the circle with equation

(2, −7)

−5

4x − 8y = 8

(−2, 4) (1, −3).

x2 + y2 − 6x + 8y + 9 = 0.

center (x, y) =

radius



4) Let be points in the plane.

(a) Find the slope of the line that contains A and B.

(b) Find an equation of the line that passes through A and B.

What are the intercepts?

(c) Find the midpoint of the segment AB.

(d) Find the length of the segment AB.

(e) Find an equation of the perpendicular bisector of AB.

(f) Find an equation of the circle for which AB is a diameter.

If you have had difficulty with these problems, you may wish to consult the Review of Analytic Geometry on the websiteStewartCalculus.com.

A(−5, 0) and B(1, −8)

x-intercept (x, y) =

y-intercept (x, y) =

(x, y) =

24. -Question Details SCalc7 0.Diagnostic.AnalyticGeometry.001a. [2742746]

Find an equation for the line that passes through the point and

has slope

If you have had difficulty with this problem, you may wish to consult the Review of Analytic Geometry on the websiteStewartCalculus.com.

(x, y) = (4, −7)

−4.

25. -Question Details SCalc7 0.Diagnostic.AnalyticGeometry.001d. [2742618]

Find an equation for the line that passes through the point and

is parallel to the line


(2, −5)

2x − 4y = 3.



26. -Question Details SCalc7 0.Diagnostic.AnalyticGeometry.002. [2742656]

Find an equation for the circle that has center and passes through the point


(−4, 3) (3, −4).


Find the center and radius of the circle with equation

center

radius


x2 + y2 − 18x + 16y + 81 = 0.

(x, y) =

8


Let be points in the plane.

(a) Find the slope of the line that contains A and B.

(b) Find an equation of the line that passes through A and B.

What are the intercepts?

(c) Find the midpoint of the segment AB.

(d) Find the length of the segment AB. 20

(e) Find an equation of the perpendicular bisector of AB.

(f) Find an equation of the circle for which AB is a diameter.


A(−12, 2) and B(0, −14)

x-intercept (x, y) =

y-intercept (x, y) =

(x, y) =



29. -Question Details SCalc7 0.Diagnostic.Functions. [1725480]

1) The graph of a function f is given.

(a) State the value of f(-1).f(-1) = -2

(b) Estimate the value of f(2).f(2) = 2.8

(c) For what values of x is f(x) = 2?x = -3 (smaller value)

x = 1 (larger value)

(d) Estimate the values of x such that f(x) = 0.x = -2.5 (smaller value)

x = 0.3 (larger value)

(e) State the domain and range of f. (If you need to use -∞ or ∞, enter -INFINITY or INFINITY.)

Domain [ -3 , 3 ]

Range [ -2 , 3 ]

2) If f(x) = x3, evaluate the difference quotient and simplify your answer.

f(2 + h) - f(2)

h

3) Find the domain of the function. (Enter your intervals in ascending order. If you need to use -∞ or ∞, enter -INFINITY orINFINITY.)

( -INFINITY , -2 ) ∪ ( -2 , 1 ) ∪( 1 , INFINITY )

( -INFINITY , INFINITY )

( -INFINITY , -1 ] ∪ [ 1 , 4 ]

4) How are the graphs of the functions obtained from the graph of f ?

(a) y = -f(x)



(b) y = 2f(x) - 1

(c) y = f(x - 3) + 2

6) Let f(x) be defined as below.

Evaluate f(-2) and f(1).f(-2) = -3

f(1) = 3

7) If f(x) = x2 + 2x - 1 and g(x) = 2x - 3, find the following functions.

(a) f g =

(b) g f =

(c) g g g =

If you have had difficulty with these problems, you may wish to consult the Review of Functions on the websiteStewartCalculus.com.

Reflect about the x-axis.

Reflect about the y-axis.

Shift 1 unit downwards.

Stretch horizontally by a factor of -1.

Stretch horizontally by a factor of 2, then shift 1 unit upward.

Stretch vertically by a factor of 1, then shift 2 units downward.

Stretch vertically by a factor of 2, then shift 1 unit downward.

Stretch horizontally by a factor of 1, then shift 2 units upward.

Shift 2 units to the right and 3 units upward.

Shift 3 units to the right and 2 units downward.

Shift 3 units to the left and 2 units upward.

Shift 3 units to the right and 2 units upward.

30. -Question Details SCalc7 0.Diagnostic.Functions.002. [1872529]

If f(x) = x3, evaluate the difference quotient and simplify your answer.

If you have had difficulty with these problems, you should look at Sections 1.1 - 1.3 of your text or YouBook.

f(7 + h) − f(7)h



31. -Question Details SCalc7 0.Diagnostic.Functions.003a. [1872491]

Find the domain of the function. (Enter your answer using interval notation.)


f(x) = 2x + 1x2 + x − 42

32. -Question Details SCalc7 0.Diagnostic.Functions.003c. [1872082]

Find the domain of the function. (Enter your answer using interval notation.)


h(x) = + 5 − x x2 − 1


How is the graph of the function obtained from the graph of f ?


y = f(x − 5) + 6

shifted 6 units to the left and 5 units upward

shifted 5 units to the left and 6 units upward

shifted 6 units to the right and 5 units upward

shifted 5 units to the right and 6 units upward

shifted 5 units to the right and 6 units downward

34. -Question Details SCalc7 0.Diagnostic.Functions.007a. [1871707]

If and find the following function.


f(x) = x2 + 3x − 4 g(x) = 3x − 8,

f g




If find the following function.


g(x) = 3x − 4,

g g g

36. -Question Details SCalc7 0.Diagnostic.Trigonometry. [1725482]

1) Convert from degrees to radians.

(a) 300° = rad

(b) -18° = rad

2) Convert from radians to degrees.

(a) 5π/6 rad = 150 °

(b) 2 rad = °

3) Find the length of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°.

cm

4) Find the exact values.

(a) tan(π/3) =

(b) sin(7π/6) =

(c) sec(5π/3) =

5) Express the lengths a and b in the figure in terms of θ.

a =

b =

6) If sin(x) = 1/3 and sec(y) = 5/4, where x and y lie between 0 and π/2, evaluate sin(x + y).

7) Find all values of x such that sin 2x = sin x and 0 x 2π. (List the answers in increasing order.)



x =

x =

x =

x =

x =

If you have had difficulty with these problems, you may wish to consult the Review of Trigonometry on the websiteStewartCalculus.com.

37. -Question Details SCalc7 0.Diagnostic.Trigonometry.003. [1872322]

Find the length of an arc of a circle with radius 36 cm if the arc subtends a central angle of

cm

If you have had difficulty with these problems, you should look at Appendix D of your text or YouBook.

20°.

38. -Question Details SCalc7 0.Diagnostic.Trigonometry.004a. [1871982]

Find the exact value.


tan π3

39. -Question Details SCalc7 0.Diagnostic.Trigonometry.004c. [1871868]

Find the exact value.


sec 5π3


If and where x and y lie between 0 and π/2, evaluate sin(x + y).


sin x = 13

sec y = ,54




Find all values of x such that sin 2x = sin x and (Enter your answers as a comma-separated list.)

x =


0 ≤ x ≤ 2π.

42. -Question Details SCalc7 QP.21.001. [1806498]

Sketch the graph of the function by first making a table of values.

H(x) = |5x|

x H(x) = |5x|

5 25

4 20

3 15

2 10

1 5

0 0



Read more about Topic 21: Special Functions



43. -Question Details SCalc7 QP.21.003.MI. [1806832]

Sketch the graph of the function by first making a table of values.

x

−3 -1

−2 -1

−1 -1

0 undefined

1 1

2 1

3 1


f(x) = 5x|5x|

f(x) = 5x|5x|




Sketch the graph of the piecewise defined function.


f(x) = −1 if x < −12 if −1 ≤ x ≤ 1−1 if x > 1




Sketch the graph of the piecewise-defined function.


f(x) = 1 − (x − 3)2, x ≤ 4

, x > 4x − 4




Graph the function.


k(x) = 4x + 2, x ≤ −14x2 − 1, −1 < x ≤ 1

1 − x2, x > 1



47. -Question Details SCalc7 1.2.008. [1874693]

Find expressions for the quadratic functions whose graphs are shown.

f(x) =

g(x) =

Solution or Explanation

Click to View Solution


Jason leaves Detroit at 1:00 PM and drives at a constant speed west along I-96. He passes Ann Arbor, 40 mi from Detroit,at 1:48 PM.

(a) Express the distance d traveled in terms of the time t (in hours) elapsed.

d(t) =

(b) Draw the graph of the equation in part (a).

http://www.webassign.net/latex2pdf/39b26b71a3177614d628e24cc72d4347.pdf



(c) What is the slope of this line? 50

What does it represent?





The slope represents the distance traveled in miles.

The slope represents the time traveled in hours.

The slope represents the car's speed in miles per hour.


The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $582 to drive480 mi and in June it cost her $742 to drive 880 mi.

(a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives asuitable model.

C(d) =

(b) Use part (a) to predict the cost of driving 1800 miles per month.$ 1110

(c) Draw the graph of the linear function.

What does the slope represent?

It represents the cost (in dollars) per mile.

It represents the fixed cost (amount she pays even if she does not drive).

It represents the distance (in miles) traveled.

It represents the cost (in dollars) of driving.

http://www.webassign.net/latex2pdf/7d3caf400b92cd9e9c725559d98b1523.pdf?epsf=1



(d) What does the C-intercept represent?

(e) Why does a linear function give a suitable model in this situation?



It represents the distance (in miles) traveled.

It represents the cost (in dollars) of driving.

It represents the fixed cost (amount she pays even if she does not drive).

It represents the cost (in dollars) per mile.

A linear function is suitable because the monthly cost is fixed despite the fact that the miles driven mayvary.

A linear function is suitable because the monthly cost increases as the number of miles drivenincreases.

A linear function is suitable because the monthly cost increases as the number of miles drivendecreases.

A linear function is suitable because the monthly cost increases even if the miles driven is constant.

http://www.webassign.net/latex2pdf/afb05d05ae05f2309b35042aac3a6e82.pdf?epsf=1




For each scatter plot, decide what type of function you might choose as a model for the data.

(a)

(b)


(a) The data appear to be periodic and a sine or cosine function would make the best model. A model of the form seems appropriate.

(b) The data appear to be decreasing in a linear fashion. A model of the form seems appropriate.

linear function, of the form

trigonometric function, of the form

exponential function, of the form

logarithmic function, of the form

root function, of the form

f(x) = mx + b

f(x) = a cos(bx) + c

f(x) = a ebx+ c

f(x) = a ln(bx) + c

f(x) = a + cbx

logarithmic function, of the form

root function, of the form

trigonometric function, of the form

exponential function, of the form

linear function, of the form

f(x) = a ln(bx) + c

f(x) = a + cbx


f(x) = a ebx+ c

f(x) = mx + b


f(x) = mx + b

51. -Question Details SCalc7 1.2.JIT.002.MI. [1875282]

Solve the equation for the indicated variable.

for x

x =

a − 5[b − 6(c − x)] = 6;

52.



-Question Details SCalc7 1.2.JIT.008. [1805154]

Match the exponential function with its graph.

(a)

(b)

(c)

f(x) = 2x − 2

f(x) = 2−x

f(x) = 2x + 1

f(x) = 2x

f(x) = 2x

f(x) = 2x − 2

f(x) = 2x + 1

f(x) = 2−x



(d)

f(x) = 2x − 2

f(x) = 2−x

f(x) = 2x + 1

f(x) = 2x

f(x) = 2x − 2

f(x) = 2x + 1

f(x) = 2−x

f(x) = 2x




Find the exponential function f(x) = ax whose graph is given.

f(x) =


Find the exponential function f(x) = ax whose graph is given.

f(x) =


Explain how each graph is obtained from the graph of

(a)

(b)

y = f(x).

y = f(x) + 3

Stretch the graph horizontally and vertically by a factor of 3.

Shift the graph 3 units to the right.

Shift the graph 3 units to the left.

Shift the graph 3 units upward.

Shift the graph 3 units downward.

y = f(x + 3)



(c)

(d)

(e)

(f)


(a) To obtain the graph of from the graph of shift the graph 3 units upward.

(b) To obtain the graph of from the graph of shift the graph 3 units to the left.

(c) To obtain the graph of from the graph of stretch the graph vertically by a factor of 3.


Shift the graph 3 units downward.


Shift the graph 3 units to the right.


y = 3f(x)

Shrink the graph horizontally by a factor of 3.




Stretch the graph vertically by a factor of 3.

y = f(3x)






y = −f(x) − 1

First reflect the graph about the x-axis, and then shift it 1 unit downward.

First reflect the graph about the x-axis, and then shift it 1 unit left.

First reflect the graph about the x-axis, and then shift it 1 unit upward.

First reflect the graph about the y-axis, and then shift it 1 unit upward.

First reflect the graph about the y-axis, and then shift it 1 unit downward.

y = 3f x13


Shrink the graph horizontally and vertically by a factor of 3.



Stretch the graph horizontally by a factor of 3.

y = f(x) + 3 y = f(x),

y = f(x + 3) y = f(x),

y = 3f(x) y = f(x),



(d) To obtain the graph of from the graph of shrink the graph horizontally by a factor of 3.

(e) To obtain the graph of from the graph of first reflect the graph about the x-axis, and thenshift it 1 unit downward.

(f) To obtain the graph of from the graph of stretch the graph horizontally and vertically by a

factor of 3.

y = f(3x) y = f(x),

y = −f(x) − 1 y = f(x),

y = 3f x13

y = f(x),

56. -Question Details SCalc7 1.3.006.MI. [1875147]

The graph of is given. Use transformations to create a function whose graph is as shown.

y =



y = 2x − x2


Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given inSection 1.2, and then applying the appropriate transformations.

y = − x7

http://www.webassign.net/latex2pdf/953761fa06d33faaca443d3e710771f5.pdf




Start with the graph of and reflect about the x-axis.y = − :x7 y = x7






Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given inSection 1.2, and then applying the appropriate transformations.


Start with the graph of reflect about the x-axis, shift 1 unit upward, and then shrink

vertically by a factor of 2.

y = (1 − cos x)12

y = (1 − cos x):12

y = cos x,




Find each of the following functions and state their domains. (Enter the domains in interval notation.)

(a)

f + g =

domain

(b)

f − g =

domain

(c)

fg =

domain

(d)

f/g =

domain



f(x) = x3 + 4x2, g(x) = 6x2 − 1

f + g

f − g

fg

f/g

http://www.webassign.net/latex2pdf/d368ca53d6d91dcc610a898816992b42.pdf




Find each of the following functions.

(a) f g

State the domain of the function. (Enter your answer using interval notation.)

(b) g f


(c) f f


(d) g g




f(x) = x2 − 1, g(x) = 2x + 2

http://www.webassign.net/latex2pdf/51a21c65e0a9d313938fcdc50a26f758.pdf





(a) f g


(b) g f


(c) f f


(d) g g




f(x) = 2 − 4x, g(x) = cos x

http://www.webassign.net/latex2pdf/3025b9b619feead1492fd6f346b308d0.pdf





(a) f g


(b) g f


(c) f f


(d) g g




f(x) = , g(x) = x 8 − x3

http://www.webassign.net/latex2pdf/f9d61b3dffe4854c7c0709e1e502f481.pdf




Find the functions and their domains. (Enter the domains in interval notation.)

(a) f g

(f g)(x) =

domain

(b) g f

(g f)(x) =

domain

(c) f f

(f f)(x) =

domain

(d) g g

(g g)(x) =

domain



f(x) = x + , g(x) = 1x

x + 17x + 2

http://www.webassign.net/latex2pdf/c72ceb901f99b9bb142e33029f2c906c.pdf





(a) f g

State the domain of the function.

(b) g f


(c) f f


(d) g g




f(x) = , g(x) = sin 3xx1 + x

x ≠ + πn [where n is any integer]π4

23


23


23

x ≠ + 7πn [where n is any integer]7π2

x ≠ + 7πn [where n is any integer]π2

http://www.webassign.net/latex2pdf/8fe53897319fcaa9be418a409cc98d6d.pdf




Find


f g h.

f(x) = 9x − 2, g(x) = sin x, h(x) = x2

(f g h)(x) = f(g(h(x))) = f(g(x2)) = f(sin(x2)) = 9 sin(x2) − 2

66. -Question Details SCalc7 1.3.041.alt. [1863785]

Express the function in the form f g. (Use only non-identity functions.)


F(x) = (7x + x2)4

{f(x), g(x)} =

Let g(x) = 7x + x2 and f(x) = x4. Then (f g)(x) = f(g(x)) = f(7x + x2) = (7x + x2)4 = F(x).


Express the function in the form (Use non-identity functions for f and g.)



f g.

G(x) = 3 x9 + x

{f(x), g(x)} =


Express the function in the form (Use non-identity functions for f and g.)



f g.

u(t) = csc t3 + csc t

{f(t), g(t)} =

http://www.webassign.net/latex2pdf/d4be0433e18fd2978b3d3df02aa79234.pdf

http://www.webassign.net/latex2pdf/98496642302deca131c20dfa53b1239a.pdf




Use the table to evaluate each expression.

x 1 2 3 4 5 6

f(x) 3 6 6 1 2 2

g(x) 2 4 6 5 2 2

(a) f(g(1)) 6

(b) g(f(1)) 6

(c) f(f(1)) 6

(d) g(g(1)) 4

(e) (g f)(3) 2

(f) (f g)(6) 6



http://www.webassign.net/latex2pdf/e5e869a2f02a1bbae7ae975dd37bd660.pdf




Use the given graphs of f and g to evaluate each expression, or if the expression is undefined, enter UNDEFINED.

(a) f(g(2)) 4

(b) g(f(0)) 3

(c) (f g)(0) 0

(d) (g f)(6) UNDEFINED

(e) (g g)(−2) 4

(f) (f f)(4) -2



http://www.webassign.net/latex2pdf/482cfcc45ca86d770ab3135eca2f552d.pdf



71. -Question Details SCalc7 1.3.054.MI. [1874675]

A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 8 cm/s.

(a) Express the radius r of the balloon as a function of the time t (in seconds).

r(t) =

(b) If V is the volume of the balloon as a function of the radius, find V r.

(V r)(t) =

Interpret the answer found in part (b).



This formula gives the amount of time (in seconds) the balloon has been inflating as a function of V.

This formula gives the volume of the balloon (in cm3) as a function of time (in seconds).


A ship is moving at a speed of 35 km/h parallel to a straight shoreline. The ship is 9 km from shore and it passes alighthouse at noon.

(a) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship hastraveled since noon; that is, find f so that

s = f(d) =

(b) Express d as a function of t, the time elapsed since noon; that is, find g so that

d = g(t) =

(c) Find f g.

(f g)(t) =

What does this function represent?



s = f(d).

d = g(t).

This function represents time elapsed since noon as a function of the distance between the lighthouseand the ship.

This function represents the distance between the lighthouse and the ship as a function of the timeelapsed since noon.

http://www.webassign.net/latex2pdf/5b9b29e7e297f0c4dc53b67de51b3da7.pdf

http://www.webassign.net/latex2pdf/5753f60e4231737498eaa4ad910bae2e.pdf?epsf=1




An airplane is flying at a speed of 350 mi/h at an altitude of one mile and passes directly over a radar station at time t = 0.

(a) Express the horizontal distance d (in miles) that the plane has flown as a function of t.

d(t) =

(b) Express the distance s between the plane and the radar station as a function of d.

s(d) =

(c) Use composition to express s as a function of t.

(s d)(t) =




The Heaviside function H is defined by

It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch isinstantaneously turned on.

(a) Sketch the graph of the Heaviside function.

(b) Sketch the graph of the voltage in a circuit if the switch is turned on at time t = 0 and 180 volts areapplied instantaneously to the circuit.

H(t) = 0 if t < 01 if t ≥ 0.

V(t)

http://www.webassign.net/latex2pdf/47261bb5be1e2e62efa3b355c7ad6347.pdf



Write a formula for V(t) in terms of H(t).

(c) Sketch the graph of the voltage in a circuit if the switch is turned on at time t = 7 seconds and 230 voltsare applied instantaneously to the circuit.

Write a formula for in terms of (Note that starting at t = 7 corresponds to a translation.)



V(t) = H(t) − 180

V(t) = 180

V(t) = 180H(t)

V(t) = H(t)180

V(t) = H(t) + 180

V(t)

V(t) H(t).

V(t) = 7H(t + 230)

V(t) = 230H(t) − 7

V(t) = 7H(t − 230)

V(t) = 230H(t + 7)

V(t) = 230H(t − 7)

http://www.webassign.net/latex2pdf/bb86c610451591fbe8e745fc333521dc.pdf?epsf=1




If you invest x dollars at 7% interest compounded annually, then the amount A(x) of the investment after one year is A(x)= 1.07x. Find A A, A A A, and A A A A.

A A =

A A A =

A A A A =

What do these compositions represent?

Find a formula for the composition of n copies of A.



They represent the amount of interest gained on the investment after 2, 3, and 4 years.

They represent the total amount of the investment after 2, 3, and 4 years.


Suppose g is an even function and let h = f g. Is h always an even function?



Yes

No

http://www.webassign.net/latex2pdf/118100fc49fbf57faef7bcd1ed60446e.pdf

http://www.webassign.net/latex2pdf/98b88c6d5d21e4b66d16d080150f5418.pdf




Suppose g is an odd function and let h = f g. Is h always an odd function?

What if f is odd?

What if f is even?



Yes

No

h is even.

h is odd.

There is not enough information to determine what h is.

h is even.

h is odd.

There is not enough information to determine what h is.

78. -Question Details SCalc7 1.3.501.XP. [1874332]

Explain how the following graphs are obtained from the graph of y = f(x). (Select all that apply.)

(a) y = 9f(x)

(b) y = f(x − 4)

Shift 9 units upward.

Shift 9 units downward.

Shift 9 units to the right.

Shift 9 units to the left.


Shrink the graph vertically by a factor of 9.




Reflect about the origin.

http://www.webassign.net/latex2pdf/5bf6123f43cf4f9849bfc2e8ff7dd882.pdf



(c) y = −f(x)

(d) y = −6f(x)

(e) y = f(4x)











Shift 1 unit upward.

Shift 1 unit downward.

Shift 1 unit to the right.

Shift 1 unit to the left.



















(f) y = 8f(x) − 6































http://www.webassign.net/latex2pdf/0ef8931c673963afb4bc5af2e92777be.pdf




Express the function in the form f g if

f(t) =



g(t) = sec t.

u(t) = sec t


Suppose f is even and g is odd. What is fg?



even

odd

81. -Question Details SCalc7 1.3.JIT.003. [1805402]

Find the domain of the function.

f(x) = x + 5x2 − 9

(-∞, ∞)

(-∞, 9) ∪ (9, ∞)

(-∞, -3) ∪ (-3, 3) ∪ (3, ∞)

(0, 9)

(-∞, -3) ∪ (3, ∞)

http://www.webassign.net/latex2pdf/16946a5b68f5b36ebb4b988939b8dc9d.pdf

http://www.webassign.net/latex2pdf/1c4fdde6ea8f2bdb2f1ab9d4ac6143cb.pdf



Name (AID): E1 (6263274)Submissions Allowed: 2Category: ExamCode:Locked: YesAuthor: Frith, Russell ( [email protected] )Last Saved: Sep 2, 2014 05:03 PM AKDTPermission: ProtectedRandomization: PersonWhich graded: Last

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82. -Question Details SCalc7 1.3.JIT.008. [2107314]

Explain how the graph of g is obtained from the graph of f. If a graph is not supposed to be stretched or shrunk, enter "1"in the corresponding box on the right. If a graph is not supposed to be shifted in some direction, enter "0" in thecorresponding box on the right.

(a) f(x) = |x|, g(x) = |x + 3| − 3

Reflect? Do not reflect

Stretch/Shrink vertically? neither stretch nor shrink vertically by a factor of 1

Stretch/Shrink horizontally? neither stretch nor shrink horizontally by a factor of 1

Shift up/down? shift down 3 unit(s)

Shift left/right? shift left 3 unit(s)

(b) f(x) = |x|, g(x) = |x − 3| + 3

Reflect? Do not reflect

Stretch/Shrink vertically? neither stretch nor shrink vertically by a factor of 1

Stretch/Shrink horizontally? neither stretch nor shrink horizontally by a factor of 1

Shift up/down? shift up 3 unit(s)

Shift left/right? shift right 3 unit(s)

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E1 (6263274) 1. Question Details SCalc7 0.Diagnostic ...rfrith.uaa.alaska.edu/Calculus/ESolns/E1_Solns_Fall2014.pdf · x 2b x 1 6a − 2b True False 2. Question Details SCalc7 0.Diagnostic.Algebra.002b