Unit 4 Class Starters.notebook€¦ · 2. Create a rational function with the following characteristics: >x‑intercepts at 1/2 and 3/4 ... Honors Precalculus March 22, 2018 Use the

Unit 4 Class Starters.notebook

1

March 22, 2018

Sep 237:45 PM

Honors PrecalculusClass StarterMarch 2, 2018

Simplify the following expressions by factoring the numerator and denominator and canceling like factors. Identify the domain.

1. 2. 3.

4. Given the function y = 2(x + 3)2(x 2)3, classify the points at x = 3 and x = 2.

5. Profit is determined by multiplying the price of a unit times the number of units sold minus the cost of producing the number of units. If the price of each unit x is given by p = 130 + 0.2x2 and the cost of producing x units is given by c = 75x + 2,000, find the "break even point" (in other words, the number of units that must be sold to get a profit of 0).

Mar 16:41 AM

Class StarterHonors PrecalculusMarch 6, 2018

Simplify the following. Identify restrictions on domains.

1. 2.

3. 4.

5. A rectangular prism has volume given by 36x3 + 9x2 100x 25 and base area given by 12x2 17x 5. What is the height of the prism?

Feb 248:12 AM


Simplify the following. Identify the restrictions on the domain in #1 and #3.

1. 2.

3.

4. Given the function .

(a) Find f(3) and f(1).

(b) Simplify the compound fraction and then find f(3) and f(1).

Sep 262:28 PM


Simplify the following expressions. Find the domain.

1. 2.

3. 4.

5. 6.

Sep 262:30 PM


Solve the following equations.

1. 2.

3. Simplify the following expressions.

(a) (b)

Oct 1212:27 PM

4. Find the vertical and horizontal asymptotes and holes of the following functions.

(a) (b)


1. Working together Billy Bob and Bubba Lee can rebuild a car engine in 3 hours. Working alone, it would take Billy Bob two hours longer than it would take Bubba Lee. How long would it take each of them to rebuild the engine if they worked alone?

2. Roxanne can clean the house twice as fast as Billy Jean can. Working together, they can clean the house 3 hours faster than Roxanne can working alone. How long would it take Billy Jean to clean the house?

3. A bathtub can be filled in 8 minutes. It takes 12 minutes for the bathtub to drain. If the faucet is turned, but the drain is left open, how long will it take to fill the tub?


2

March 22, 2018

Mar 92:29 PM


1. Identify all asymptotes and holes in the following functions, if any exist. Then identify the intercepts.

(a) (b)

2. Create a rational function with the following characteristics:xintercepts at x = 3 and x = 0hole at x = 4vertical asymptotes at x = 2 and x = 1horizontal asymptote at y = 3

3. Simplify the following using long division:

Feb 2511:10 AM


1. Solve the following equation:

2. If F is the focal length of a convex lens and an object is placed at a distance x from the lens, then its image will be at a distance y from the lens, where F, x, and y are

related by the equation . Suppose that a lens has a focal length

of 4.8 cm, and that the image of an object is 4 cm closer to the lens than the object itself. How far from the lens is the object?

3. In anticipation of a large rain storm, a reservoir needs to have the water level reduced by one foot. Pipe A can reduce the water level in 4 hours. Smaller pipe B takes 6 hours to reduce the water level to this height. How long would it take both pipes working together to reduce the water level?

Mar 217:05 AM


1. A drug is administered to a patient and the concentration of the drug in the bloodstream is monitored. At time t > 0 (in hrs since giving the drug), the concentration (in mg/L) is given by . Graph the function on your calculator and answer the following questions. (a) What is the drug concentration after two hours?

(b) When is the drug concentration at its maximum and what is the highest concentration? (c) What happens to the drug concentration after a long period of time? Justify your answer.

2. Create a rational function with the following characteristics:> x‑intercepts at 1/2 and 3/4> hole at x = 3> vertical asymptotes at x = 1 and x = 5> horizontal asymptotes at y = ‑3

3. Graph the following function:

Oct 178:45 PM


Use the function to find the given expressions.

1.

2.

3.

Mar 611:13 AM


1. Find the average rate of change in the following expressions over the given interval.

(a)

(b)

2. Find the average rate of change in the function below over the interval [3,5]. Then find the equation of the secant line to the curve through those points.

3. Find the equation of the secant lines to the curves below when a = 3 & h = .01.

(a) (b)

Mar 31:17 PM


1. Find the intervals over which the function is increasing and over which the function is decreasing. Identify any extreme values.

2. Use the difference quotient to find the average rate of change in the following functions. Then find the equation of the secant line when a = 1 and h = 0.5.

(a) (b)

3. The distance a particle has traveled is given by , where d is measured in feet and t in seconds. Find the average speed of the particle over each interval. How fast do you think the particle is moving at exactly t = 2 seconds?

(a) [2,3] (b) [2,2.5] (c) [2,2.1] (d) [2,2.01]

4. Find the equation of the tangent line to the curve at x = 1.


3

March 22, 2018

Mar 31:17 PM


See class starter handout

Nov 74:14 PM


1. The intensity of illumination I from a light varies inversely as the square of the distance d from the light. If it is known that a lamp has an intensity of 1000 candles at a distance of 8 meters, what is the intensity of this lamp at a distance of 20 meters.

2. The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h, and inversely proportional to its length L. A beam 4 in wide, 6 in high, and 12 ft long can support a weight of 4800 lb. If a 10 ft beam made of the same material is 3 in wide and 10 in high, what is the maximum weight it can support?

3. During a thunderstorm you see the lightning before you hear the thunder because light travels much faster than sound. The distance between you and a storm is proportional to the time interval between the lightning and the thunder. If the thunder from a storm 5400 ft away occurs 5 seconds after the lightning flashes, how far away is the same storm when the time interval between the lightning and thunder is 8 seconds.

Attachments

10310.doc

10510.docx

Name: _______________________________________

AP Calculus

Class Starter: October 3, 2010

Assume that f(x), g(x), and h(x) are differentiable functions. Use the table of data to evaluate the following derivatives.

x

f(x)

f ′(x)

g(x)

g′(x)

h(x)

h′(x)

-2

-5

8

0

-2

11

-8

-1

-9

1

2

-4

17

-5

0

11

12

-8

0

-1

2

1

1

16

-8

-2

-12

-6

2

-4

2

7

-8

1

-5

3

0

-9

4

13

-18

1

1.

(

)

(

)

2

fg

¢

+

2.

(

)

(

)

1

fg

¢

-

3.

(

)

0

h

g

¢

æö

ç÷

èø

4.

(

)

(

)

3

hf

¢

5. Let

(

)

(

)

(

)

mxfgx

=

. Find

(

)

1

m

¢

-

.

6. Let

(

)

(

)

x

nxegx

=

. Find

(

)

1

n

¢

.

7. Let

(

)

(

)

(

)

3

fx

kx

gx

=

. Find

(

)

2

k

¢

-

.

8. Let

(

)

(

)

2

pxxhx

=

. Find

(

)

0

p

¢

.

9. Let

(

)

(

)

(

)

rxhgx

=

. Find

(

)

1

r

¢

.

10. Let

(

)

(

)

(

)

3

gx

sx

fx

éù

ëû

=

. Find

(

)

3

s

¢

.

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SMART Notebook

Honors Precalculus

Class Starter

October 4, 2010

x

f(x)

g(x)

h(x)

-2

-4

1

1

-1

0

-3

-1

0

-7

5

0

1

-3

0

-2

2

6

-3

-7

3

1

2

2

Use the data in the table above to evaluate the following.

1. f ( g(-2) )2. ( g ◦ f ) (3)3. h ( g ( f(3) ) )

4. f-1(-7)5. h-1(-2)6. f-1( g(1) )

7. Does g(x) have an inverse? Explain your answer.

8. Do all functions have an inverse? Do all linear functions have an inverse? Is the inverse of a function also a function?

SMART Notebook

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Unit 4 Class Starters.notebook€¦ · 2. Create a rational function with the following characteristics: >x‑intercepts at 1/2 and 3/4 ... Honors Precalculus March 22, 2018 Use the