Slide 2 - 1 MAT 171 Chapter 2 Review The following is a brief review of Chapter 2 for Test 2 that covers Chapters 2 & 3 and Section 10.7. This does NOT

Slide 2 - 1

MAT 171 Chapter 2 Review

The following is a brief review of Chapter 2 for Test 2 that covers Chapters 2 & 3 and Section 10.7. This does NOT cover all the material that may be on the test.

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Dr. Claude Moore, Math Instructor, CFCC

Slide 2 - 2

Active Learning Lecture SlidesFor use with Classroom Response Systems

© 2009 Pearson Education, Inc.

Chapter 2

Copyright © 2009 Pearson Education, Inc. Slide 2 - 3

Chapter 2: More on Functions

2.1 Increasing, Decreasing, and Piecewise Functions; Applications

2.2 The Algebra of Functions

2.3 The Composition of Functions

2.4 Symmetry and Transformations

2.5 Variation and Applications


a. (0, 1)

c. (3, 0)

b. (4, 3)

d. (1, 2)

Determine the interval on which the function is increasing.


a. (0, 1)

c. (3, 0)

b. (4, 3)

d. (1, 2)

Determine the interval on which the function is increasing.


a. rel max 0 at x = 0; rel min 4 at x = –32

c. rel max 32 at x = 4; rel min 0 at x = 0

b. rel max 0 at x = 0; rel min –32 at x = 4

d. There are no relative extrema.

Use a graphing calculator to find any relative maxima or minima of

f x x3 6x2 .


a. rel max 0 at x = 0; rel min 4 at x = –32

c. rel max 32 at x = 4; rel min 0 at x = 0

b. rel max 0 at x = 0; rel min –32 at x = 4

d. There are no relative extrema.

Use a graphing calculator to find any relative maxima or minima of

f x x3 6x2 .


a.

c.

b.

d.

Trisha and Gordon drive away from a campground at right angles to each other. Trisha’s speed is 70 mph and Gordon’s speed is 55 mph. Express the distance between the cars as a function of time.

f t 1875 gt 2

f t 1875 gt

f t 7925 gt

f t 7925 gt 2


a.

c.

b.

d.

Trisha and Gordon drive away from a campground at right angles to each other. Trisha’s speed is 70 mph and Gordon’s speed is 55 mph. Express the distance between the cars as a function of time.

f t 1875 gt 2

f t 1875 gt

f t 7925 gt

f t 7925 gt 2


a.

c.

b.

d.

Which piecewise function matches the graph?

f (x)

2 for 3 x 0

2 x2 for 0 > x

2x 4 for x 3

f (x)

2 for 0 x 2

2 x2 for x 0

2x 4 for x 2

f (x)

2 x2 for x 0

2 for 3 x 0

2x 4 for x 3

f (x)

2x 4 for x 2

2 x2 for x 0

2 for 0 x 2


a.

c.

b.

d.

Which piecewise function matches the graph?

f (x)

2 for 3 x 0

2 x2 for 0 > x

2x 4 for x 3

f (x)

2 for 0 x 2

2 x2 for x 0

2x 4 for x 2

f (x)

2 x2 for x 0

2 for 3 x 0

2x 4 for x 3

f (x)

2x 4 for x 2

2 x2 for x 0

2 for 0 x 2


a. 2

c. 7

b. 0

d. 5

Find f (–1) if

f x x2 1, for x 3

x 6 , for 3 x 1

3x , for x 1


a. 2

c. 7

b. 0

d. 5

Find f (–1) if

f x x2 1, for x 3

x 6 , for 3 x 1

3x , for x 1


a. 5

c. 1

b.

d. 4

Find f (2) if f x x2 1, for x 3

x 6 , for 3 x 1

3x , for x 1

6


a. 5

c. 1

b.

d. 4

Find f (2) if f x x2 1, for x 3

x 6 , for 3 x 1

3x , for x 1

6


a. x + 5

c. x2 + 5

b. x2 – x – 1

d. x2 + x + 5

Given that f (x) = x + 3 and g (x) = x2 + 2, find ( f + g) x.


a. x + 5

c. x2 + 5

b. x2 – x – 1

d. x2 + x + 5

Given that f (x) = x + 3 and g (x) = x2 + 2, find ( f + g) x.


a.

c.

b.

d.

Given that f (x) = x2 – 4 and

, find the domain of g/f .g x 3 x

, 3

, 3

, 2 2,2 2,

, 2 2,2 2, 3


a.

c.

b.

d.

Given that f (x) = x2 – 4 and

, find the domain of g/f .g x 3 x

, 3

, 3

, 2 2,2 2,

, 2 2,2 2, 3


a. 3

c. –7h

b. –7

d. 3 – 7x – 7h

Construct and simplify the difference quotient for f (x) = –7x + 3.


a. 3

c. –7h

b. –7

d. 3 – 7x – 7h

Construct and simplify the difference quotient for f (x) = –7x + 3.


a. 2x + 6

c. 2xh + h2 + 6h

b. x2 + 2xh + 6x + h2 + 6h

d. 2x + h + 6

Construct and simplify the difference quotient for f (x) = x2 + 6x.


a. 2x + 6

c. 2xh + h2 + 6h

b. x2 + 2xh + 6x + h2 + 6h

d. 2x + h + 6

Construct and simplify the difference quotient for f (x) = x2 + 6x.


a. h(x) = 2x2 + 4

c. h(x) = 2x2 + 16x + 32

b. h(x) = 2x3 + 8x2

d. h(x) = 2x2 + x + 4

For f(x) = x + 4 and g(x) = 2x2, find

h x gof .


a. h(x) = 2x2 + 4

c. h(x) = 2x2 + 16x + 32

b. h(x) = 2x3 + 8x2

d. h(x) = 2x2 + x + 4

For f(x) = x + 4 and g(x) = 2x2, find

h x gof .


a.

c.

b.

d.

For and g(x) = x2, find

the domain of

f x 14 x

f og x .

, 4 4,

, 2 2,2 2,

,2 2,

,16 16,


a.

c.

b.

d.

For and g(x) = x2, find

the domain of

f x 14 x

f og x .

, 4 4,

, 2 2,2 2,

,2 2,

,16 16,


a.

c.

b.

d.

For f(x) = 3x – 4 and g(x) = , find h(x) = (fg)(x).

x

h(x) 3x 4 x

h(x) x 3x 4

h(x) 3 x 4

h(x) 3x 4


a.

c.

b.

d.

For f(x) = 3x – 4 and g(x) = , find h(x) = (fg)(x).

x

h(x) 3x 4 x

h(x) x 3x 4

h(x) 3 x 4

h(x) 3x 4


a.

c.

b.

d.

Which of the following is symmetric with respect to the origin?

y (x 4)2

x y2

y x 2

y x x3


a.

c.

b.

d.

Which of the following is symmetric with respect to the origin?

y (x 4)2

x y2

y x 2

y x x3


a.

c.

b.

d.

Which of the following functions is even?

y 16 x2

y 2x3

y 4x 6

y x


a.

c.

b.

d.

Which of the following functions is even?

y 16 x2

y 2x3

y 4x 6

y x


a.

c.

b.

d.

Write an equation for a function that has the shape of but is shifted left 3 units and down 5 units.

y x ,

f (x) x 3 5

f (x) x 5 3

f (x) x 3 5

f (x) x 5 3


a.

c.

b.

d.

Write an equation for a function that has the shape of but is shifted left 3 units and down 5 units.

y x ,

f (x) x 3 5

f (x) x 5 3

f (x) x 3 5

f (x) x 5 3


a.

c.

b.

d.

If (3, 6) is a point on the graph of y = f (x), what point do you know is on the graph of y = f (x + 3)?

( 6,6)

( 3,9)

(0,6)

(0,9)


a.

c.

b.

d.

If (3, 6) is a point on the graph of y = f (x), what point do you know is on the graph of y = f (x + 3)?

( 6,6)

( 3,9)

(0,6)

(0,9)


a.

c.

b.

d.

The graph of y = f (x) is given. Which graph below represents the graph of y = f (x) – 1?


a.

c.

b.

d.

The graph of y = f (x) is given. Which graph below represents the graph of y = f (x) – 1?


a.

c.

b.

d.

The graph of f is given. Which graph below represents the graph of g(x) = 2f (x) + 1?


a.

c.

b.

d.

The graph of f is given. Which graph below represents the graph of g(x) = 2f (x) + 1?


a.

c.

b.

d.

Which of the following is symmetric with respect to the y-axis?

f (x) 5 x2

f (x) x

f (x) 5x3

f (x) x


a.

c.

b.

d.

Which of the following is symmetric with respect to the y-axis?

f (x) 5 x2

f (x) x

f (x) 5x3

f (x) x


a. 2

c. 2

b. 72

d.

If y varies inversely as x and y = 12 when x = 30, find y when x = 5.

1

72


a. 2

c. 2

b. 72

d.

If y varies inversely as x and y = 12 when x = 30, find y when x = 5.

1

72


a. 33.6 in3

c. 32.0 in3

b. 56.8 in3

d. 72.3 in3

The volume of a 6-in. tall cone varies directly as the square of the radius. The volume is 14.2 in3 when the radius is 1.5 in. Find the volume when the radius is 3 in.


a. 33.6 in3

c. 32.0 in3

b. 56.8 in3

d. 72.3 in3

The volume of a 6-in. tall cone varies directly as the square of the radius. The volume is 14.2 in3 when the radius is 1.5 in. Find the volume when the radius is 3 in.


a.

c.

b.

d.

Find an equation of variation where y varies jointly as the square of x and the square of z and inversely as w, and y = 50 when x = 2, z = 3, and w = 10.

y 9x2z2

36wy

250w

x2z2

y 36x2z2

9wy

125x2z2

9w


a.

c.

b.

d.

Find an equation of variation where y varies jointly as the square of x and the square of z and inversely as w, and y = 50 when x = 2, z = 3, and w = 10.

y 9x2z2

36wy

250w

x2z2

y 36x2z2

9wy

125x2z2

9w


a. 0.5

c. 15.2

b. 12.5

d. 0.08

If y varies inversely as x and y = 0.2 when x = 10, find y when x = 25.


a. 0.5

c. 15.2

b. 12.5

d. 0.08

If y varies inversely as x and y = 0.2 when x = 10, find y when x = 25.


a. 0.25 ampere

c. 0.16 ampere

b. 1.25 ampere

d. 0.08 ampere

The current I in an electrical conductor varies inversely as the resistance R of the conductor. Suppose I is 0.2 amperes when the resistance is 200 ohms. Find the current when the resistance is 250 ohms.


a. 0.25 ampere

c. 0.16 ampere

b. 1.25 ampere

d. 0.08 ampere

The current I in an electrical conductor varies inversely as the resistance R of the conductor. Suppose I is 0.2 amperes when the resistance is 200 ohms. Find the current when the resistance is 250 ohms.

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Slide 2 - 1 MAT 171 Chapter 2 Review The following is a brief review of Chapter 2 for Test 2 that covers Chapters 2 & 3 and Section 10.7. This does NOT