# Math 135 Fall Test

Directions: No Calculator . Do all your work on these pages (Use the back if needed). Place your answers in the appropriate spaces. Simplify all answers as much as possible. Budget your time. Look at the test and do your best.

1. Give the domain of the following:

a.

b.

c.

2. For find f(f(x)).

3. For the graph below , find the following:

a. f(-1)
b. the value of x for f (x) = 5 |

4. Graph the following :

5. For

a. find

b. find

6. Find for the function

7. If the graph of f (x) is translated down 2 units, and across the y - axis, what is the equation of the graph ?

a.-f(x -2)

b. f(-x) -2

c. f(-x -2)

d. -f(x) -2

8. Graph y =

9. For f(x) = 3x -5 and

a. find

b. give the domain of

c. find

d. find

10. For f(x) =
,
and g(x) =
*
*find the domain of
.

11. For

a. find f(2)

b. find f^{-1}(x)

c. solve for x : f^{-1}(x) = 2

12. Find the linear equation with the following properties: f(3) = 7, f(7) = -3.

13. Find the vertex , determine if it is a max. or min. point, find the axis of symmetry and the intercepts of the following:

a.

vertex____________

( circle one ) Max Min.

axis of symmetry____________

x-intercepts____________

y-intercepts____________

b.

vertex____________

( circle one ) Max Min.

axis of symmetry____________

x-intercepts____________

y-intercepts____________

14. If the total volume of a right circular cylinder must be 32 oz. express the surface area as a function of the radius.

15. For a right circular cone the volume is V =
.
If the volume of the cone is 12π
cm^{3}, express the height as a function of the radius.

16. Find the x value of the point on the graph of y =
*
*which is closest to the point (5,0), and find the
minimal distance.

Point = ______________Distance = ____________

17. 2 numbers add up to 11. Find the largest possible value for their product.

18. Graph :

a. f(x) = (x - 3)(x + 2)(x - 1)

b. f(x) = (x - 3)(x + 2)(x -1)^{2}

19. Graph . Clearly show the asymptotes and important points:

a.

b.

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