4. From a 24-inch by 24-inch piece of metal, squares are cut out of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of x. Graph the function and from the graph determine the value of x, to the nearest tenth of an inch, that will yield the maximum volume.

a. 3.6 inches

b. 4.0 inches

c. 4.2 inches

d. 3.8 inches

6. Given that f(x)=x220 and g(x)=6x+1, find (fg)-1/6, if it exists.

Select the correct choice below.

A.(fg)(-)= _____ (simplify answer)

or

B. The value for(fg)(1/6) does not exist.

7. For the pair of functions, find the indicated sum, difference, product, or quotient.

f(x)=2x2, g(x)=7x8

Find (fg)(x).

a. -5x+6

b. 5x-6

c. 9x-10

d. -5x-10

8. For the pair of functions, find the indicated sum, difference, product, or quotient.

f(x)=7+x, g(x)=4|x|

Find (gf)(x).

a. 7+x/4|x|

b. 4|x|-7+x

c. 4|x/7 + x

d. 4|x|/7+x

9. For the pair of functions, find the indicated domain.

f(x)=2x5, g(x)= square root x+2

Find the domain of fg

a. [2,)

b. (2,2)

c. [0,)

d. (2,)

10. For the pair of functions, find the indicated domain.

For f(x)= square root of x3 and g(x)= 1/x-7

Find the domain of fg.

a. [0,7)(7,)

b. [3,)

c. [3,7)(7,)

d. (3,7)(7,)

11. For the function f, construct and simplify the difference quotient

f(x+h)f(x)/h

.

f(x)= 1/7x

a. 1/x (x+h)

b. 1/7x

c. 0

d. -1/7x(x+h)

13. For the pair of functions, find the indicated composition.

f(x)=4x2+5x+4, g(x)=5x6

Find (gf)(x).

a. 4x2+5x+20

b. 20x2+25x+26

c. 4x2+25x+14

d. 20x2+25x

15. Find f(x) and g(x) such that h(x) =(fg)(x).

h(x)=7/square root 8x+4

a. f(x)=7/x, g(x)=8x+4

b. f(x)= square root 8x+4, g(x)=7

c. f(x)=7/square root x, g(x)= 8x+4

d. f(x)=7, g(x)= square root 8x+4

17. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

6x6y=0

Select all that apply.

a. symmetric to the y-axis

b. symmetric to the origin

c. symmetric to the x-axis

d. not symmetric to the x-axis, y-axis, or origin

18.Find the point that is symmetric to (13,4) with respect to the x-axis, the y-axis, and the origin.

The point symmetric to (13,4) with respect to the x-axis is _____ (in ordered pair)

The point symmetric to (13,4) with respect to the y-axis is ____(in ordered pair)

The point symmetric to (13,4) with respect to the origin is: response here ___(in ordered pair)

19. Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x)=6/x2

20. How can the graph of f(x)=6x3+8 be obtained from the graph of y=x3?

a. Stretch it horizontally by a factor of 8. Reflect it across the x-axis. Shift it 6 units upward.

b. Stretch it horizontally by a factor of 6. Reflect it across the x-axis. Shift it 8 units downward.

c. Stretch it vertically by a factor of 6. Reflect it across the x-axis. Shift it 8 units upward.

d. Stretch it vertically by a factor of 6. Reflect it across the y-axis. Shift it 8 units upward.

21. How can the graph of f(x) = (x+10)2 7 be obtained from the graph of y=x2?

a. Shift it horizontally 10 units to the right. Stretch it vertically by a factor of 2. Shift it 7 units up.

b. Shift it horizontally 10 units to the right. Shrink it vertically by a factor of . Shift it 7 units down.

c. Shift it horizontally 10 units to the left. Shrink it vertically by a factor of . Shift it 7 units down.

d. Shift it horizontally 10 units to the left. Shrink it vertically by a factor of 2. Shift it 7 units down.

22. The given point is on the graph of y =f(x). Find a point on the graph of y=g(x).

g(x)=f(x)3; (8,22)

a. (8,19)

b. (8,20)

c. (8,23)

d. (8,17)

23. Input equation for a function that has a graph with the given characteristics.

The shape of y=3 square root of x is shifted 4.2 units to the left. This graph is then vertically stretched by a factor of 3.7. Finally, the graph is reflected across the x-axis.

a. f(x)=3.73 square root of x4.2

b. f(x) =4.23 square root of x+3.7

c. f(x) = 3.73 square root of x+4.2

d. f(x)= 3.73 square root of x+4.2