MATH 22 NAME

EXAM I STUDENT NUMBER

INSTRUCTOR

SAMPLE E SECTION NUMBER

On your scantron, write and bubble your PSU ID, Section Number, and Test Version. Failureto correctly code these items may result in a loss of 5 points on the exam.

On your scantron, bubble letters corresponding to your answers on indicated questions. Itis a good idea for future review to circle your answers in the test booklet.

Check that your exam contains 20 questions numbered sequentially.

Answer Questions 1-20 on your scantron.

Each multiple choice question is worth 5 points.

THE USE OF A CALCULATOR, CELL PHONE, OR ANYOTHER ELECTRONIC DEVICE IS NOT PERMITTED IN THISEXAMINATION.

THE USE OF NOTES OF ANY KIND IS NOT PERMITTEDDURING THIS EXAMINATION.

MATH 22 EXAM I, SAMPLE E PAGE 2

1. Solve for x:x

5− 2 =

x

2+ 3.

a) x = −50

3

b) x =50

3

c) x = −3

2

d) x =3

2

e) x = −5

3

2. Solve for x:2

x + 3− 7

x− 3=

3

x2 − 9.

a) x = 10

b) x = 30

c) x = −6

d) x = −8

e) There is no solution.

3. What number must be added to x2− 5x to “complete the square” and turn it into a perfectsquare trinomial?

a) 25

b)25

2

c)5

2

d)5

4

e)25

4

MATH 22 EXAM I, SAMPLE E PAGE 3

4. Solve for x: x2 + 7x + 5 = 0.

a) x =7±√

29

2

b) x =−7±

√29

14

c) x =−7± 69

2

d) x =−7±

√29

2

e) x =−7± i

√13

2

5. Solve for x: x4 − 11x2 + 18 = 0.

a) x = −3, 3,√

2, −√

2

b) x = 3,√

2

c) x = 9, 2

d) x = −9, 9, −2, 2

e) x = −3, 3

6. Solve for x:√

6x + 27 = x.

a) x = 9

b) x = −9

c) x = −3, x = 9

d) x = −9, x = 3

e) There is no real solution.

MATH 22 EXAM I, SAMPLE E PAGE 4

7. Solve for x: |9x− 1|+ 4 = 9.

a) x = −8

9, x =

10

9

b) x = −5

9, x =

5

9

c) x = −4

9, x =

2

3

d) x = −2

3, x =

4

9

e) x = −10

9, x =

8

9

8. Solve for x: x2 − 10x > x− 28

a) (4, 7)

b) (−7,−4)

c) (−∞,−7) ∪ (4,∞)

d) (−∞, 4) ∪ (7,∞)

e) (−∞,−4) ∪ (7,∞)

9. Solve for x:x− 4

x + 6< 1.

a) (−∞,−6)

b) (−6,∞)

c) (−∞,−6) ∪ (4,∞)

d) (−6, 4)

e) (4,∞)

MATH 22 EXAM I, SAMPLE E PAGE 5

10. If f(x) = x2 + 6x, find the difference quotientf(x + h)− f(x)

h.

a)2xh + h2 + 12x + 6h

h

b) 2x + h + 6

c) 2x + h

d) 2x + 6

e) 1

11. What is the domain of f(x) =x

x2 + 4?

a) (−∞,−4) ∪ (−4, 4) ∪ (4,∞)

b) (−∞,−2) ∪ (−2, 2) ∪ (2,∞)

c) (−∞, 0 ∪ (0,∞)

d) (2,∞)

e) (−∞,∞)

12. Using graph transformations, sketch the graph of f(x) = (−x + 1)2 + 2. Which of thefollowing is TRUE?

a) The graph of f(x) has a relative MAXIMUM at x = 1.

b) The graph of f(x) has a relative MINIMUM at x = 2.

c) The function f(x) is even.

d) The graph of f(x) is increasing on (1,∞).

e) The graph of f(x) is increasing on (−∞,−1).

MATH 22 EXAM I, SAMPLE E PAGE 6

13. Which function is even?

a) f(x) = 8x3 − 9

b) f(x) =√x

c) f(x) = |x− 1|

d) f(x) =x

x2 + 2

e) f(x) = x4 − x2

14. What is the range of

f(x) =

{|x| if − 2 ≤ x < 1;

1 if 1 ≤ x ≤ 5.?

a) [−2, 5]

b) [−2, 1]

c) [0, 2]

d) (1, 2]

e) [0, 1)

MATH 22 EXAM I, SAMPLE E PAGE 7

15. Which piecewise function best matches the graph below?

-1.0 -0.5 0.5 1.0 1.5 2.0

0.5

1.0

1.5

2.0

2.5

3.0

a) f(x) =

{√x + 1 if − 1 ≤ x < 1;

x2 − 1 if 1 ≤ x ≤ 2.

b) f(x) =

{√−x + 1 if − 1 ≤ x < 1;

x2 if 1 ≤ x ≤ 2.

c) f(x) =

{√−x + 1 if − 1 ≤ x < 1;

x2 − 1 if 1 ≤ x ≤ 2.

d) f(x) =

{√x− 1 if − 1 ≤ x < 1;

x2 + 1 if 1 ≤ x ≤ 2.

e) f(x) =

{√−x− 1 if − 1 ≤ x < 1;

(x + 1)2 if 1 ≤ x ≤ 2.

MATH 22 EXAM I, SAMPLE E PAGE 8

16. Beginning with the graph of f(x) = |x|, shifting to the right by 1 unit, stretching verticallyby a factor of 3, then reflecting about the y-axis, you will obtain the graph of which function?

a) g(x) = −|3x− 1|

b) g(x) = −3|x− 1|

c) g(x) = −1

3|x− 1|

d) g(x) = −3|x + 1|

e) g(x) = 3| − x− 1|

17. The graph of a function f(x) is below. Using graph transformations, find the range of thefunction −f(x) + 1.

H2, 1L

H3, -1LH0, -3L

-1 1 2 3 4

-4

-2

2

4

a) [−1, 3]

b) [0, 3]

c) [0, 4]

d) [−2, 2]

e) [1, 4]

MATH 22 EXAM I, SAMPLE E PAGE 9

18. If f(x) =√x and g(x) = x− 1, what is the domain of

f

g(x)?

a) [0,∞)

b) (0, 1) ∪ (1,∞)

c) (1,∞)

d) [0, 1) ∪ (1,∞)

e) (−∞, 1) ∪ (1,∞)

19. The graph of a function f(x) is given below. Find the value of (f ◦ f)(1).

-3 -2 -1 1 2 3

-2

-1

1

2

3

4

5

6

a) 4

b) 2

c) 1

d) 0

e) −1

MATH 22 EXAM I, SAMPLE E PAGE 10

20. Which function is one-to-one?

a) f(x) = (x + 1)2

b) f(x) = −|x|

c) f(x) =1

x− 1

d) f(x) = 0

e) f(x) = −x2 − 5

1. A2. C3. E4. D5. A6. A7. C8. D9. B10. B11. E12. D13. E14. C15. C16. B17. C18. D19. A20. C