precalculus honors name chapter 4 test review date · pdf fileprecalculus honors name_____...

Precalculus Honors Name________________________

Chapter 4 Test Review Date_________________________

1. The graph of f(x) is given below. On separate axes, graph:

a. f(-x) b. –f(x) c. ( )f x d. f(x) +2

2. If 2( )f x x and ( ) 2 3g x x , determine the domain of f g x and g f x given:

a. The domain of f(x) = (-3, 5) and the domain of g (x)= (- , ).

b. The domain of f(x) = [0, ) and the domain of g(x)= [-1,1].

c. The domain of f(x) = (-9,9) and the domain if g(x)=(- ,0].

3. Make a sketch of the following functions; include in your sketch the key points and any

asymptotes.

a. 2 3 5 4f x x b. 2

43 2

g xx



4. State whether the function f(x) has an inverse. If 1f x exists, find a rule for 1f x

and show that 1 1f f x f f x x .

a. 25f x x

b. 2

1 1, 1f x x x

c. 3 4 2f x x

5. Given 5f x x , find 1f x

a. Find x such that 1f x f x

6. The surface area, A, of a cube is a function of the length of a side, s, of a face.

a. Express A as a function of s.

b. Find A(9).



7. Given the graph of f(x) below, if f x Af B x C D :

a. How will a B value of ½ affect the graph of f(x)?

b. How will an A value of -3 affect the graph of f(x)?

c. How will a B value of -1 affect the graph of f(x)?

d. Describe how various values of C and D affect not just f(x) but any function.

8. If 2

1( )

2f x

x

and 25g x x

a. Determine f g x

b. Determine g f x

c. Determine the domain of f g x .

d. Sketch a graph of f g x , indicating any vertical or horizontal asymptotes.

9. If 2 5, [ 3,4)f x x x and 2 3, ( 1,7]g x x x .

a. Determine the domain of f g x .

b. Determine the domain of g f x .



10. If 2

3 5 3, ( ,5]f x x x

a. Determine 1f x .

b. Make a sketch of f x and 1f x on the same set of axes indicating any key

points.

c. Prove that 1f x is an inverse of f x by showing algebraically that

1 1f f x x or f f x x

11. A balloon is inflated in such a way that its volume increases at a rate of 20 3 /cm s .

a. If the volume of the balloon was 100 3cm when the process of inflation began,

what will the volume be after t seconds of inflation?

b. Assuming that the balloon is spherical while it is being inflated, express the

radius, r, of the balloon as a function of t. 34

3sphereV r



12. A cylindrical soda pop can of radius r and height h is to hold exactly

500 ml of liquid when completely full. A manufacturer wishes to

find the dimensions of the can with minimum surface area.

a. Show that the surface area of the can is 22 2S r rh .

b. Use the fact that the volume of the can is 2500 r h to

determine the surface area as a function of the radius.

c. Draw a complete graph of the function S of part b.

d. What are the restrictions on r in order for the graph to

represent the problem situation?

e. Use zoom in to determine the radius r and height h that yield a can of minimal

surface area. What is the minimal surface area?

f. Why might this problem be important to a manufacturer?

g. What other factors might be considered in choosing r and h?

13. An automobile race track is to be constructed in the shape of

two parallel section connected by two semicircles. The track

(one round trip) is to be exactly 2.5 miles in length.

a. Write an equation for the area of the shaded rectangular

region as a function of the radius r.

b. Draw a complete graph of the function in part a.

c. What values of r make sense in this problem situation?

d. Use a graph to determine the value of the radius that produces the maximum

rectangular area. What is the maximum rectangular area?



14. A single story house with rectangular base is to contain 900

square feet of living area. Local building codes require that

both the length and the width of the base of the house be

greater than 20 feet. To minimize the cost of the foundation,

the builder desires to minimize the perimeter of the

foundation.

a. Determine an equation that gives the perimeter as a

function of L, the length of the base.

b. Draw a complete graph of the function in part a.

c. What are the possible values of L that make sense in

this problem situation? Draw a graph of the problem situation.

d. Use a graph to determine the values of L that minimize the perimeter. What is the

minimum perimeter?

precalculus honors name chapter 4 test review date · pdf fileprecalculus honors name_____...

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