Determine the domain and range of the piecewise 1.

Domain [–3, 3]; Range [0, 3]
Domain [–3, 3]; Range [–2, 4]
Domain [–2, 4]; Range [–3, 3]
Domain [–1, 4]; Range [–2, 2]

Solve:

= x – 3

No solution B. 11/2
5
-2, 5

Determine the interval(s) on which the function is 3.

(–¥, –1)

(– 4.5, – 1) and (2.5, ¥)

(–¥, – 3) and (1, ¥) D. (– 2, 2)

Determine whether the graph of

y = 8 – x

is symmetric with respect to the origin,

the x-axis, or the y-axis. 4.

symmetric with respect to the x-axis only
symmetric with respect to the y-axis only
symmetric with respect to the origin only
1. Determine the domain and range of the piecewise 1.
1. Domain [–3, 3]; Range [0, 3]
2. Domain [–3, 3]; Range [–2, 4]
3. Domain [–2, 4]; Range [–3, 3]
4. Domain [–1, 4]; Range [–2, 2]
1. Solve:
= x – 3
1. No solution B. 11/2
2. 5
3. -2, 5
1. Determine the interval(s) on which the function is 3.
1. (–¥, –1)
1. (– 4.5, – 1) and (2.5, ¥)
1. (–¥, – 3) and (1, ¥) D. (– 2, 2)
1. Determine whether the graph of
y = 8 – x

is symmetric with respect to the origin,
the x-axis, or the y-axis. 4.
1. symmetric with respect to the x-axis only
2. symmetric with respect to the y-axis only
3. symmetric with respect to the origin only
4. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin
1. Solve, and express the answer in interval notation: | 3 – 8x | £ 21.
1. [–9/4, 3]
2. (–¥, -9/4] È [3, ¥)
3. (–¥, –9/4]
4. [–9/4, ¥)
1. Which of the following represents the graph of 3x – 7y = 21 ?
1. D.
1. Write a slope-intercept equation for a line parallel to the line x – 4y = 2 which passes through the point (8, –1).
1. y = – 4x + 31
1. y = 1 x -1 4
1. y = 1 x – 3 4
1. y = – 1 x +1 4
1. Which of the following best describes the graph?
1. It is the graph of a function and it is one-to-one.
2. It is the graph of a function and it is not one-to-one.
3. It is the graph of an absolute value
4. It is not the graph of a
1. Express as an equivalent expression: log x + log 1 – 4 log y
log ç x +1 ÷

æ ö
1. ç ÷
è ø

æ x ö

y
- log ç 4 ÷
è ø

4

æ x +1 ö
1. log
ç y ÷

è ø
1. log ( x +1-4 y )
1. Which of the functions corresponds to the graph?
1. f (x) = e– x + 2
2. f (x) = –ex + 3
3. f (x) = e– x + 3
4. f (x) = ex + 3
1. Suppose that a function f has exactly one x-intercept.
Which of the following statements MUST be true? 11.
1. f is a linear
2. f (x) ³ 0 for all x in the domain of f.
3. The equation f (x) = 0 has exactly one real-number
4. f is an invertible
1. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the (No formulas are given.) What is the relationship between g(x) and f (x)?
y = f (x) y = g(x)
1. g(x) = f (x – 2)
2. g(x) = f (x + 2)
3. g(x) = f (x – 4)
4. g(x) = f (x) – 2
SHORT ANSWER:
1. Multiply and simplify: (5 + 7i)2.
Write the answer in the form a + bi, where a and b are real numbers. Answer:
1. Solve, and write the answer in interval notation: x + 4 ³ 0 . Answer:
x +1
1. A can of soda at 81° is placed in a refrigerator that maintains a constant temperature of 38°
2. The temperature T of the soda t minutes after it is placed in the refrigerator is given by
T(t) = 38 + 43e – 0.058 t

Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the nearest tenth of a degree.)

Answer:

æ 1 ö

è ø
- Find the value of the logarithm: log7 ç49 ÷. Answer:
1. Solve:
86x+1 = 64 . Answer:
1. Suppose $5,400 is invested in an account at an annual interest rate of 3.3% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:
1. Let f (x) = x2 + 8x + 9.
- Find the Answer:
- State the range of the Answer:
- On what interval is the function decreasing? Answer:
1. Consider the polynomial P(x), shown in both standard form and factored
P(x) = – 1 x3 – 3 x2 + 13 x + 3 = – 1 (x – 3)(x +1)(x + 5)

5 5 5 5

A.

vvvv
B.

vvvv
C.

vvvv
D.

vvvv
- Which sketch illustrates the end behavior of the polynomial function?
Answer:
- State the y-intercept. Answer:
- State the zeros of the Answer:
- State which graph below is the graph of P(x). Answer: GRAPH A GRAPH B
GRAPH C GRAPH D
1. Let
f (x) = 5x .

x2 – 9
- State the Answer:
- State the horizontal Answer:
- State the vertical asymptote(s). Answer:
- Which of the following represents the graph of
f (x) =    5x x2 – 9

?         Answer:
GRAPH A.                                                               GRAPH B.

GRAPH C.                                                              GRAPH D.

SHORT ANSWER, with work required to be shown, as indicated.
1. Let
f (x) =

and g(x) = x – 3.
æ f ö
- Find çç ÷÷(-1) . Show work.
è g ø
- Find the domain of the quotient function f .
g
1. Points (–1, 0) and (–9, –8) are endpoints of the diameter of a
- What is the length of the diameter? Give the exact answer, simplified as much as
Show work.
- What is the center point C of the circle?
- Given the point C you found in part (b), state the point symmetric to C about the x-axis.
1. Find the equation for a line which passes through the points (5, –3) and (2, 9). Write the equation in slope-intercept form. Show
1. Nick, a resident of Metropolis, pays Metropolis an annual tax of $60 plus 5% of his annual income. If Nick paid $930 in tax, what was Nick’s income? Show work.
1. Let f (x) = 7x2 + 5 and g(x) = x – 3.
- Find the composite function ( f o g)(x) and simplify. Show
- Find ( f o g ) (2) . Show
1. Find the exact solutions and simplify as much as possible: 2x2 + 3 = 6x. Show
1. Given the function f (x) = 1 x – 6 , find a formula for the inverse function. Show
7
1. The fuel efficiency F for a particular car is given by
F(x) = –0.016 x2 + 1.44 x + 5.4

where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).
- What is the fuel efficiency if the car’s speed is 20 mph?
- What speed will yield the maximum fuel efficiency? Show
1. Solve:
x – 8 + 30 = 0 . Show work.

Solve, and express the answer in interval notation: | 3 – 8x | £ 21.

[–9/4, 3]
(–¥, -9/4] È [3, ¥)
(–¥, –9/4]
[–9/4, ¥)

Which of the following represents the graph of 3x – 7y = 21 ?

Write a slope-intercept equation for a line parallel to the line x – 4y = 2 which passes through the point (8, –1).

y = – 4x + 31

y = 1 x -1 4

y = 1 x – 3 4

y = – 1 x +1 4

Which of the following best describes the graph?

It is the graph of a function and it is one-to-one.
It is the graph of a function and it is not one-to-one.
It is the graph of an absolute value
It is not the graph of a

Express as an equivalent expression: log x + log 1 – 4 log y

log ç x +1 ÷

æ ö

ç ÷

è ø

æ x ö

log ç 4 ÷

è ø

æ x +1 ö

ç y ÷

è ø

log ( x +1-4 y )

Which of the functions corresponds to the graph?

f (x) = e– x + 2
f (x) = –ex + 3
f (x) = e– x + 3
f (x) = ex + 3

Suppose that a function f has exactly one x-intercept.

Which of the following statements MUST be true? 11.

f is a linear
f (x) ³ 0 for all x in the domain of f.
The equation f (x) = 0 has exactly one real-number
f is an invertible

The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the (No formulas are given.) What is the relationship between g(x) and f (x)?

y = f (x) y = g(x)

g(x) = f (x – 2)
g(x) = f (x + 2)
g(x) = f (x – 4)
g(x) = f (x) – 2

SHORT ANSWER:

Multiply and simplify: (5 + 7i)2.

Write the answer in the form a + bi, where a and b are real numbers. Answer:

Solve, and write the answer in interval notation: x + 4 ³ 0 . Answer:

x +1

A can of soda at 81° is placed in a refrigerator that maintains a constant temperature of 38°
The temperature T of the soda t minutes after it is placed in the refrigerator is given by

T(t) = 38 + 43e – 0.058 t

Find the temperature of the soda 20 minutes after it is placed in the refrigerator. (Round to the nearest tenth of a degree.)

Answer:

æ 1 ö

è ø

Find the value of the logarithm: log7 ç49 ÷. Answer:

Solve:

86x+1 = 64 . Answer:

Suppose $5,400 is invested in an account at an annual interest rate of 3.3% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

Let f (x) = x2 + 8x + 9.

Find the Answer:

State the range of the Answer:

On what interval is the function decreasing? Answer:

Consider the polynomial P(x), shown in both standard form and factored

P(x) = – 1 x3 – 3 x2 + 13 x + 3 = – 1 (x – 3)(x +1)(x + 5)

5 5 5 5

vvvv

Which sketch illustrates the end behavior of the polynomial function?

Answer:

State the y-intercept. Answer:

State the zeros of the Answer:

State which graph below is the graph of P(x). Answer: GRAPH A GRAPH B

GRAPH C GRAPH D

f (x) = 5x .

x2 – 9

State the Answer:

State the horizontal Answer:

State the vertical asymptote(s). Answer:

Which of the following represents the graph of

f (x) = 5x x2 – 9

? Answer:

GRAPH A. GRAPH B.

GRAPH C. GRAPH D.

SHORT ANSWER, with work required to be shown, as indicated.

f (x) =

and g(x) = x – 3.

æ f ö

Find çç ÷÷(-1) . Show work.

è g ø

Find the domain of the quotient function f .

Points (–1, 0) and (–9, –8) are endpoints of the diameter of a

What is the length of the diameter? Give the exact answer, simplified as much as

Show work.

What is the center point C of the circle?
Given the point C you found in part (b), state the point symmetric to C about the x-axis.

Find the equation for a line which passes through the points (5, –3) and (2, 9). Write the equation in slope-intercept form. Show

Nick, a resident of Metropolis, pays Metropolis an annual tax of $60 plus 5% of his annual income. If Nick paid $930 in tax, what was Nick’s income? Show work.

Let f (x) = 7x2 + 5 and g(x) = x – 3.

Find the composite function ( f o g)(x) and simplify. Show
Find ( f o g ) (2) . Show

Find the exact solutions and simplify as much as possible: 2x2 + 3 = 6x. Show

Given the function f (x) = 1 x – 6 , find a formula for the inverse function. Show

The fuel efficiency F for a particular car is given by

F(x) = –0.016 x2 + 1.44 x + 5.4

where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).

What is the fuel efficiency if the car’s speed is 20 mph?

What speed will yield the maximum fuel efficiency? Show

Solve:

x – 8 + 30 = 0 . Show work.