Graphs and Functions

The rational expressions are multiplied. Simplify:
Show some work. 1. ______

A. 0

B. 1

C.

D.

Which of the following is TRUE about the line through the points (-3, 7) and (-3, 2)? EXPLAIN/SHOW WORK. 2. _______
A. The slope is negative.
B. The slope is 0.
C. The slope is positive.
D. The slope is undefined.

Find the slope-intercept equation of the line parallel to the line x + y = 7 and containing the point (-2, 5). EXPLAIN/SHOW WORK. 3. _______

A. y = - x + 3
B. y = - x + 5
C. y = x + 5
D. y = x + 7

The nation's total credit card charges increased from $69 billion in 1989 to $1800 billion in 2006. Find the average rate of change of total credit card charges per year.
Show work/explanation. 4. _______
A. Approximately $87 billion per year
B. Approximately $93 billion per year
C. Approximately $102 billion per year
D. Approximately $112 billion per year

Given , determine the domain. (no explanation required) 5. _______

A. All real numbers except 1
B. All real numbers except - 4 and 4
C. All real numbers except - 4, 1, and 4
D. All real numbers except 1 and 4

Describe how the graph of the function g(x) = |x - 2| - 6 can be obtained from the graph of the function f(x) = |x|. (no explanation required) 6. _______

A. Shift the graph of f(x) = |x| by 8 units down.
B. Shift the graph of f(x) = |x| by 2 units down, reflect across the y-axis and shift 6 units up.
C. Shift the graph of f(x) = |x| by 2 units to the left and 6 units down.
D. Shift the graph of f(x) = |x| by 2 units to the right and 6 units down.

Let f(x) = 4x3. Which of the following is true? 7. _______
(no explanation required)
A.
B.
C.
D. None of the above

For #8 and #9 consider the following graph of a function y = f(x). (Assume that the domain is all real numbers and the graph continues beyond the graph window.)

8. (3 pts) Referring to the graph, what is true about the graph's symmetry? (no explanation required)

8. _______

A. symmetric with respect to the x-axis
B. symmetric with respect to the y-axis
C. symmetric with respect to the origin
D. symmetric with respect to the x-axis, the y-axis, and the origin

9. (3 pts) Referring to the graph, for what x values is the function f increasing? (no explanation required)

9. _______

A. (- , -3.5)  (0, 3.5)
B. (- 5.3, 5.3)
C. (- 3.5, 0)
D. (- 2, 2)

Suppose you take a piece of cardboard measuring 10 inches by 10 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x. (no explanation required)
10. _______

A. V(x) = x2 (5 - x)

B. V(x) = x (10 - x)2

C. V(x) = x (10 - 2x)2

D.

Let and . 11. _______

Find the composite function . Show work.

A.

B.

C.

D.

Simplify (10 + 5i)2 and write the answer in the form a + bi, where a and b are real numbers. Show work.
12. _______
A. 75
B. 75 + 100i
C. 125 + 100i
D. 100 + 125i

Find the solutions of the equation 5x2 + x - 4 = 0. Show work. 13. _______

A.

B. ,

C. ,

D. ,

SHORT ANSWER QUESTIONS (5 problems)

Simplify . Show some work.

The points (7, -5) and (1, 3) are endpoints of the diameter of a circle.

(a) State the center of the circle.

(b) Find the length of the radius of the circle. (Note that this is a distance.) Give the exact answer. Show work.

(c) State the equation of the circle (in standard form). Note that you know the center and the radius from the previous parts.

A graph of the y = f (x) follows. No formula for f is given.

(a) From looking at the graph, state the value of f (-3).

(b) State the domain.

(c) State the range.
.

(d) The piecewise function has three pieces. Write the formula for just ONE PIECE of this piecewise function. (You choose the piece you prefer.)

f(x) = ___________________ for __________________ (state the x-values associated with your piece).

Consider the equation x2 - 2x + 10 = 0.

(a) Compute the discriminant, b2 - 4ac and state whether there is one real-number solution, or two different real-number solutions, or two different imaginary-number solutions.

(b) Use the quadratic formula to find the exact solutions of the equation. Show work.

An investment advisor invested a total of $10,000, part at 5% annual simple interest and part at 3.5% annual simple interest. The amount of interest earned for 1 year was $437. How much was invested at the 5% rate and how much was invested at the 3.5% rate?

Show work for this problem by defining variables, writing appropriate equation(s), and showing the solving process. Write a sentence to answer the question. (Use more paper as needed)