# Expert Answers

#1-12 are Multiple Choice.

#13-21 are Short Answer. (Work not required to be shown)

#22-30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function.

A. Domain [-4, 2]; Range [-3, 3]

B. Domain

[-4, 2]; Range [-2, 1]

C. Domain [-3, 3]; Range [-4, 2]

D. Domain

[-2, 1]; Range [-4, 2]

2. Solve:

.J4x+21 = -x

A. -3,7

B. -3

c. -2115

D. No solution

4

1. __ _

2. __ _

Page 1 of 11

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

A. (--00, -1)

B. (- 2, 2)

C. (- 4.5, - 1) and (2.5, oo)

D. (--00, - 3) and (1, oo)

-6

4

4. Determine whether the graph of y = !x+ 21 is symmetric with respect to the origin, the x-axis, or the y-axis. 4. __ _

A. symmetric with respect to the x-axis

only

B. symmetric with respect to they-axis only

C. symmetric with respect to the origin only

D. not symmetric with respect to the x-axis, not symmetric with respect to they-axis, and not symmetric with respect to the origin

5. Solve,

and express the answer in interval notation: I 6- 5x I~ 14.

6. Which of the following represents the graph of 3x + 8y = 24 ?

7. Write a slope-intercept equation for a line parallel to the line x + 8y = 3 which passes through the point

8. Which of the following best describes the graph?

A. It is the graph of a function and it is one-to-one.

B. It is the graph of a function and it is not one-to-one.

C. It is not the graph

of a function and it is one-to-one.

D.

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

8. __ _

Page 4 of ll

9. Express as a single logarithm: log x + log 1-6log y

log(x+ 1J

1Y

log ( x + 1-6 y)

10. Which of the functions corresponds to the graph?

8

-2 2

4

6

A.

f(x)=e-x+2

B.

f(x)=ex +2

C.

f(x)=e-x+l

D.

f(x)=-ex +2

9. __

10. __ _

Page 5 of 11

11. Suppose that a function/ has exactly one x-intercept.

Which of the following statements MUST be true?

A. f is a linear function.

B. f(x) ~ 0 for all x in the domain off

C. f is an invertible function.

D. The equationf(x) = 0 has exactly one real-number solution.

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

g(x) andf(x)?

2

4

Y = f(x)

y=g(x)

A. g(x) = f(x + 2) + 2

B. g(x) = f(x + 2)- 1

C. g(x) = f(x- 2) - 1

D. g(x) = f(x + l)- 2

11.

__ _

12. __ _

Page 6 of II

SHORT ANSWER:

13. Multiply and simplify: (4 + 5i)(7 + 2i).

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

14. Solve, and write the answer in interval notation: x- 6 x-2 ~ 0.

15. A bowl of soup at 170° F. is placed in a room of constant temperature of 60° F. The

Temperature T of the soup t minutes after it is placed in the room is given by T(t) = 60 + 110 e -o.o 15 1

Find the temperature of the soup 6 minutes after it is placed in the room. (Round to the nearest degree.)

16. Find the value of the logarithm: log

17. Solve:

18. Suppose $9,200 is invested in an account at an annual interest rate of 1.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

19.

Letf(x) = ~ + 6x + 21.

(a) Find the vertex.

Answer:

(b) State the range of the function.

Answer:

(c)

On what interval is the function decreasing?

Answer:

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

1 4 3 3 3 2 13 1

P(x) = -x --x +-x +-x-6=-(x+2)(x-1)(x-3)(x-4)

4 2 4 2 4

(a) Which sketch illustrates the end behavior of the polynomial function?

(b) State they-intercept.

(c) State the zeros of the function.

(d) State which graph below is the graph of P(x).

GRAPH A

(a) State the domain. Answer: --------

(b) State the vertical asymptote(s). Answer: --------

(c) State the horizontal asymptote. Answer: --------

(d) Which of the following represents the graph of f(x) = ~~

Let f(x) = .Jx-1 and g(x) = x- 8.

(a) Find (; } 5). Show work.

(b) Find the domain of the quotient function f . Explain.

23. Points (2, 1) and (8, -3) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.

Show work.

(b) What is the center point C of the circle?

(c) Given the point

C you found in part (b), state the point symmetric to C about the x-axis.

24. Find the equation for a line which passes through the points (3, -7) and (-1, 9). Write the equation in slope-intercept form.

Show work.

25. A salesperson earns a base salary of $2,100 per month and a commission of 6.5% on the Amount of sales made. If the salesperson has a paycheck of $3,868 for one month, what was the Amount of sales for the month? Show work.

26. Let/ (x) = 2x 2 + 9 and g(x) = x- 2.

(a) Find the composite function(/ o g)(x)and simplify. Show work.

(b) Find (fog )(-4). Show work.

27. Find the exact solutions and simplify as much as possible: 5x

28.

Given the function f(x) =.!. x-6 ; find a formula for the inverse function. Show work.

29. The fuel efficiency F for a particular car is given by

F(x) = -0.018 :l + 1.656 x + 4.4 where xis the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).

(a) What is the fuel efficiency if the car's speed is 25 mph?

(b) What speed will yield the maximum fuel efficiency? Show work.

#13-21 are Short Answer. (Work not required to be shown)

#22-30 are Short Answer with work required to be shown.

MULTIPLE CHOICE

1. Determine the domain and range of the piecewise function.

A. Domain [-4, 2]; Range [-3, 3]

B. Domain

[-4, 2]; Range [-2, 1]

C. Domain [-3, 3]; Range [-4, 2]

D. Domain

[-2, 1]; Range [-4, 2]

2. Solve:

.J4x+21 = -x

A. -3,7

B. -3

c. -2115

D. No solution

4

1. __ _

2. __ _

Page 1 of 11

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

A. (--00, -1)

B. (- 2, 2)

C. (- 4.5, - 1) and (2.5, oo)

D. (--00, - 3) and (1, oo)

-6

4

4. Determine whether the graph of y = !x+ 21 is symmetric with respect to the origin, the x-axis, or the y-axis. 4. __ _

A. symmetric with respect to the x-axis

only

B. symmetric with respect to they-axis only

C. symmetric with respect to the origin only

D. not symmetric with respect to the x-axis, not symmetric with respect to they-axis, and not symmetric with respect to the origin

5. Solve,

and express the answer in interval notation: I 6- 5x I~ 14.

6. Which of the following represents the graph of 3x + 8y = 24 ?

7. Write a slope-intercept equation for a line parallel to the line x + 8y = 3 which passes through the point

8. Which of the following best describes the graph?

A. It is the graph of a function and it is one-to-one.

B. It is the graph of a function and it is not one-to-one.

C. It is not the graph

of a function and it is one-to-one.

D.

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

8. __ _

Page 4 of ll

9. Express as a single logarithm: log x + log 1-6log y

log(x+ 1J

1Y

log ( x + 1-6 y)

10. Which of the functions corresponds to the graph?

8

-2 2

4

6

A.

f(x)=e-x+2

B.

f(x)=ex +2

C.

f(x)=e-x+l

D.

f(x)=-ex +2

9. __

10. __ _

Page 5 of 11

11. Suppose that a function/ has exactly one x-intercept.

Which of the following statements MUST be true?

A. f is a linear function.

B. f(x) ~ 0 for all x in the domain off

C. f is an invertible function.

D. The equationf(x) = 0 has exactly one real-number solution.

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

g(x) andf(x)?

2

4

Y = f(x)

y=g(x)

A. g(x) = f(x + 2) + 2

B. g(x) = f(x + 2)- 1

C. g(x) = f(x- 2) - 1

D. g(x) = f(x + l)- 2

11.

__ _

12. __ _

Page 6 of II

SHORT ANSWER:

13. Multiply and simplify: (4 + 5i)(7 + 2i).

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

14. Solve, and write the answer in interval notation: x- 6 x-2 ~ 0.

15. A bowl of soup at 170° F. is placed in a room of constant temperature of 60° F. The

Temperature T of the soup t minutes after it is placed in the room is given by T(t) = 60 + 110 e -o.o 15 1

Find the temperature of the soup 6 minutes after it is placed in the room. (Round to the nearest degree.)

16. Find the value of the logarithm: log

17. Solve:

18. Suppose $9,200 is invested in an account at an annual interest rate of 1.9% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer:

19.

Letf(x) = ~ + 6x + 21.

(a) Find the vertex.

Answer:

(b) State the range of the function.

Answer:

(c)

On what interval is the function decreasing?

Answer:

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

1 4 3 3 3 2 13 1

P(x) = -x --x +-x +-x-6=-(x+2)(x-1)(x-3)(x-4)

4 2 4 2 4

(a) Which sketch illustrates the end behavior of the polynomial function?

(b) State they-intercept.

(c) State the zeros of the function.

(d) State which graph below is the graph of P(x).

GRAPH A

(a) State the domain. Answer: --------

(b) State the vertical asymptote(s). Answer: --------

(c) State the horizontal asymptote. Answer: --------

(d) Which of the following represents the graph of f(x) = ~~

Let f(x) = .Jx-1 and g(x) = x- 8.

(a) Find (; } 5). Show work.

(b) Find the domain of the quotient function f . Explain.

23. Points (2, 1) and (8, -3) are endpoints of the diameter of a circle.

(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.

Show work.

(b) What is the center point C of the circle?

(c) Given the point

C you found in part (b), state the point symmetric to C about the x-axis.

24. Find the equation for a line which passes through the points (3, -7) and (-1, 9). Write the equation in slope-intercept form.

Show work.

25. A salesperson earns a base salary of $2,100 per month and a commission of 6.5% on the Amount of sales made. If the salesperson has a paycheck of $3,868 for one month, what was the Amount of sales for the month? Show work.

26. Let/ (x) = 2x 2 + 9 and g(x) = x- 2.

(a) Find the composite function(/ o g)(x)and simplify. Show work.

(b) Find (fog )(-4). Show work.

27. Find the exact solutions and simplify as much as possible: 5x

28.

Given the function f(x) =.!. x-6 ; find a formula for the inverse function. Show work.

29. The fuel efficiency F for a particular car is given by

F(x) = -0.018 :l + 1.656 x + 4.4 where xis the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg).

(a) What is the fuel efficiency if the car's speed is 25 mph?

(b) What speed will yield the maximum fuel efficiency? Show work.

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