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Exam

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Compute the indicated values of the given function. 1) f (x) = 4x - 7; f (0), f (-3), f (8)

A) f (0) = 0; f (-3) = -10; f (8) = 1 B) f (0) = -7; f (-3) = -10; f (8) = 1 C) f (0) = -7; f (-3) = -19; f (8) = 25 D) f (0) = 0; f (-3) = -19; f (8) = 25

1)

2) f (x) = -4x + 5; f (0), f (-9), f (6) A) f (0) = 0; f (-9) = 41; f (6) = -19 B) f (0) = 0; f (-9) = -4; f (6) = 11 C) f (0) = 5; f (-9) = -4; f (6) = 11 D) f (0) = 5; f (-9) = 41; f (6) = -19

2)

3) f (t) = 5 7 - 6t

; f (1), f (-7), f (0)

A) f (1) = 1 5

; f (-7) = 5 7

; f (0) = 5 7

B) f (1) = 5; f (-7) = 5 7

; f (0) = 5 7

C) f (1) = 5; f (-7) = 5 7

; f (0) = 5 7

D) f (1) = 1 5

; f (-7) = 5 7

; f (0) = 5 7

3)

Determine the domain of the given function.

4) g(x) = x 2 + 5

x + 9 A) All real numbers x except x = 5 B) All real numbers x except x = -9 C) All real numbers x except x = 9 D) All real numbers x except x = -5

4)

5) g(x) = x 2 + 3 x - 7

A) All real numbers x except x = -7 B) All real numbers x except x = 7 C) All real numbers x except x = 3 D) All real numbers x except x = -3

5)

6) f (x) = 4x + 20 A) All real numbers x for which x ≥ 0 B) All real numbers x for which x ≤ -5 C) All real numbers x for which x ≥ -5 D) All real numbers x for which x < -5

6)

1

Find the difference quotient, f (x + h) - f (x) h

.

7) f (x) = 5x - x2

A) f (x + h) - f (x) h

= 5 + 2x + h2 B) f (x + h) - f (x) h

= 5 - 2x - h2

C) 1 D) f (x + h) - f (x) h

= 5 - 2x - h

7)

Solve the problem. 8) Suppose the total cost of manufacturing q units of a certain product is C(q) thousand

dollars, where C(q) = 0.03q2 + 0.6q + 4. Find the total cost and the average cost of producing 10 units.

A) C(10) = $130,000; AC = $13,000 per unit B) C(10) = $13; AC = $1.30 per unit C) C(10) = $13,000; AC = $130,000 per unit D) C(10) = $13,000; AC = $1300 per unit

8)

9) The demand function p = D(x) = -0.3x + 33 and the total cost function C(x) = 1.2x2 + 9.2x + 65 for a particular commodity are given in terms of the level of production x. a. Find the revenue R(x) and profit P(x). b. Find all values of x for which production of the commodity is profitable.

A) a. R(x) = -0.3x2 + 33; P(x) = 1.5x2 - 23.8x + 65 b. 3.51 < x < 12.36

B) a. R(x) = -0.3x2 + 33x; P(x) = 1.5x2 - 23.8x + 65 b. x > 3.51

C) a. R(x) = -0.3x2 + 33; P(x) = -1.5x2 + 23.8x - 65 b. x > 3.51

D) a. R(x) = -0.3x2 + 33x; P(x) = -1.5x2 + 23.8x - 65 b. 3.51 < x < 12.36

9)

10) Arthur, the manager of a furniture factory, finds that the cost of producing q bookcases during the morning production run is C(q) = q2 + q + 500 dollars. On a typical workday, q(t) = 20t bookcases are produced during the first t hours of a production run for 0 ≤ t ≤ 5. a. Express the production cost C in terms of t. b. Arthur's budget allows no more than $4000 for production during the morning production run. When will this limit be reached?

A) a. C(t) = 400t2 + 20t + 500 b. t = 2.98 hrs

B) a. C(t) = 20t2 + 20t + 10,000 b. t = 2.93 hrs

C) a. C(t) = 20t2 + 20t + 10,000 b. t = 2.98 hrs

D) a. C(t) = 400t2 + 20t + 500 b. t = 2.93 hrs

10)

2

Classify each function as a polynomial, a power function, or a rational function. If the function is not one of these type, classify it as "different."

11) a. f (x) = x2.3

b. g(x) = (3x - 5)(7 - x)2 A) a. Power function

b. Polynomial B) a. Power function

b. Different C) a. Rational function

b. Polynomial D) a. Rational function

b. Different

11)

Sketch the graph of the given function. Include all x and y intercepts. 12) f (x) = 3x + 5

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

A) f (x) = 3x + 5; 5 3

, 0 ; (0, 5)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

B) f (x) = 3x + 5; (5, 0); 0, - 5 3

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

12)

3

C) f (x) = 3x + 5; - 5 3

, 0 ; (0, 5)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

D) f (x) = 3x + 5; (5, 0); 0, 5 3

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

13) f (x) = -x2 + 7x - 6

x-8 -4 4 8

y

8

4

-4

-8

A) f (x) = -x2 + 7x - 6 (-6, 0); (0, -6), (0, -1)

x-8 -4 4 8

y

8

4

-4

-8

B) f (x) = -x2 + 7x - 6 (1, 0), (6, 0); (0, -6)

x-8 -4 4 8

y

8

4

-4

-8

13)

4

C) f (x) = -x2 + 7x - 6 (-6, 0); (0, 1), (0, 6)

x-8 -4 4 8

y

8

4

-4

-8

D) f (x) = -x2 + 7x - 6 (-6, 0), (-1, 0); (0, -6)

x-8 -4 4 8

y

8

4

-4

-8

14) f (x) = - 1 3

x3

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

A) f (x) = - 1 3

x3; (0, 0)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

B) f (x) = - 1 3

x3; (0, 0)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

14)

5

C) f (x) = - 1 3

x3; (0, 0)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

D) f (x) = - 1 3

x3; (0, 0)

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

15) f (x) = -2x - 1 if x < 1 -3 if x ≥ 1

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

A) f (x) = -2x - 1 if x < 1 -3 if x ≥ 1

x intercept -3

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

B) f (x) = -2x - 1 if x < 1 -3 if x ≥ 1

x intercept -1; y intercept - 1 2

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

15)

6

C) f (x) = -2x - 1 if x < 1 -3 if x ≥ 1

y intercept -3

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

D) f (x) = -2x - 1 if x < 1 -3 if x ≥ 1

x intercept - 1 2

; y intercept -1

x-5 -4 -3 -2 -1 1 2 3 4 5

y 5 4 3 2 1

-1 -2 -3 -4 -5

7