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36 MCQs for Final Examination - College Algebra | MAT 110, Exams of Algebra

Piedmont Technical College Algebra

Material Type: Exam; Class: College Algebra; Subject: Mathematics; University: Piedmont Technical College; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

koofers-user-jle 🇺🇸

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Name ____________________________________ Course MAT 110 Final Exam

_____ 1. Use a graphing utility to graph

yx x x=−−

[A]

–10 10

–10

10 [B]

–10 10

–10

[C]

–10 10

–10

10 [D] none of these

______ 2. Use a graphing utility to graph yx=−–.54

[A]

–10 10

–10

10 [B]

–10 10

–10

[C]

–10 10

–10

10 [D]

–10 10

–10

Partial preview of the text

Download 36 MCQs for Final Examination - College Algebra | MAT 110 and more Exams Algebra in PDF only on Docsity!

Name ____________________________________ Course MAT 110 Final Exam

_____ 1. Use a graphing utility to graph (^) y = x^3 − x^2 −2. x

[A]

–10 10

[B]

–10 10

[C]

–10 10

[D] none of these

______ 2. Use a graphing utility to graph (^) y = – 5 x − 4.

[A]

–10 10

[B]

–10 10

[C]

–10 10

[D]

–10 10

______3. Use a graphing utility to graph x^ y

2 2 36 9

[A]

−10 10

−

[B]

−10 10

−

[C]

−10 10

−

[D]

−10 10

−

_____ 4. The total charge of a monthly phone bill, b , is given by (^) b = 26 + 015. m where $26 is the service fee and $0.15 is the cost per minute m of long distance calls. a. Sketch the graph of this equation for up to and including 120 minutes of long distance calls made in one month. b. Estimate the bill if 80 minutes of long distance calls are made.

[A] a.

(^0 50 )

b (^) [B] a.

(^0 50 )

b. $38.00 b. $38.

Evaluate the function at the specified value(s) of the independent variable and simplify.

_____9. f b g x = x + 1; f b g 5

[A] 6 [B] 4 [C] –4 [D] –

Evaluate the function at the specified value(s) of the independent variable and simplify.

_____10. f b g x = 2 x^2 − 4 x ; f b g 3

[A] 11.072 [B] 14.536 [C] 12 [D] 6

Find the domain of the function.

_____11. f x x^ x

b g x x

= +^ +

2 2

[A] All real numbers (^) x ≠ 5, – 6 [B] All real numbers x ≠ – 5 6,

[C] All real numbers (^) x ≠ 8 1, [D] All real numbers x ≠ – 8 , – 1

Find the domain of the function.

_____12. f b g x = − 3 x + 1

[A] (^) x ≥ 1 3

[B] (^) x ≤ 1 3

[C] (^) x ≤ 0 [D] (^) x ≥ 0

_____ 13. Verna plans to decorate baskets to sell at a crafts fair. The decorations cost $29. and the baskets cost $5.75 each. Let x be the number of baskets decorated. (a) Write the cost C of the project as a function of x. (b) Determine the cost of decorating 30 baskets. (c) How many baskets can be decorated with a budget of $259.00?

[A] (a) C x b g = 5 75 29 00. +.

(b) $34. (c) 43

[B] (a) C x b g = 29 00. x +5 75.

(b) $875. (c) 42

[C] (a) C x b g = 5 75. x +29 00.

(b) $201. (c) 40

[D] (a) C x b g = 5 75. x

(b) $172. (c) 41

_____14. Determine the intervals on which the function is increasing, decreasing, or constant.

–10 10

y = − b x − 3 g 2 + 1

[A] Increasing on b 3 , ∞ g; Decreasing on b− ∞, 3 g

[B] Increasing on b – 1 , ∞ g; Decreasing on b− ∞, – 1 g

[C] Increasing on b − ∞, 3 g; Decreasing on b 3 ,∞g

[D] Increasing on b 1 , ∞ g; Decreasing on b− ∞, 1 g

_____15. Determine the intervals on which the function is increasing, decreasing, or constant.

–10 10

[C]

–10 10

[D]

–10 10

_____18. Describe the transformation that occurs in the function.

g x b g b = x + 2 g^2 + 4

[A] a horizontal shift of f b g x = x^2 two units to the right and a vertical shift of y 4 units upward

[B] a horizontal shift of two units to the right and a vertical shift of y 4 units downward

f b g x = x^2

[C] a horizontal shift of f b g x = x^2 two units to the left and a vertical shift of y 4 units downward

[D] a horizontal shift of f b g x = x^2 two units to the left and a vertical shift of y 4 units upward

_____19. Find b f + g gb g x and b f + g gb 3 gfor and

f b g x = 5 x^2 + x + 5 g x b g = − 2 − 5 x + 3 x 2.

[A] 8 x^2 − 4 x + ; 63 [B] (^3) x^2 − 4 x + 8 ; 23

[C] (^3) x^2 − 4 x + 8 ; 60 [D] 8 x^2 − 4 x + 3 ; 17

_____20. Find f g

F x

HG^

I

KJb g^

for f b g x = 4 − x^2 and g x b g = 2 − x.

[A] (^) − x^2 + x + 2 [B] (^) − x^2 − x + 6

[C] (^) x^3 − 2 x^2 − 4 x + 8 [D] 2 + x

_____ 21. If f b g x = 2 − x and g x b g = 3 x + 4 , find (a) b f D g gb x g and (b)b g D f gb x g.

[A] (a) (^) − 3 x − 2 (b) (^) − 3 x + 10

[B] (a) (^) − 2 x − 6 (b) 3 x − 2

[C] (a) 2 x + 6 (b) (^) − 3 x − 2

[D] (a) (^3) x + 2 (b) 2 x + 6

_____22. Are the following functions inverses? If not, rewrite the second function so that it is an inverse of the first.

f b g x = 2 x +^1

g x b g = 1 x −

[A] Yes [B] No; g x b g = 2 x −

[C] No; g x b g = 3 x +

[D] No; g x b g = 1 x +

Find the inverse of the function.

_____ 23. f b g x = 3 x − 1

[A] f −^1 b g x = x − 1 [B] f −^1 x = 1 x −

b g

[C] f −^1 x = 1 x + 3

b g D]^ f^ −^1 b g x^ =^ x +^1

_____ 25. For the graph of the quadratic function, find the direction of the opening and the coordinates of the vertex.

f b g b x = x − 4 g^2 − 1

[A] Upward; b 4 , – 1 g [B] Upward;b – 4 , 1 g

[C] Downward; b 4 , – 1 g [D] Downward;b– 4 , 1 g

_____ 26. Find the graph of the quadratic function and list any x- intercepts.

f b g x = x^2 − 4 x + 2

[A]

−10 10

−

[B]

−10 10

−

No x - intercepts d 2 + 2 , 0 ,i d 2 − 2 , 0i

[C]

−10 10

−

[D]

−10 10

−

d 2 +^2 , 0 ,i d^2 −^2 , 0i b^ −^3 , 0 ,^ g b^ −^1 , 0g

_____27. Find all real zeros of the polynomial function.

f b g x = − 6 x^4 + 150 x^2

[A] (^) x = 0, x = 5 [B] (^) x = 0 , x = ± 5

[C] (^) x = 0 , x = 25 [D] (^) x = 0 , x = ± 25

_____28. Factor (^2) x^3^ + 3 x^2 − 11 x − 6 given that (^) x + 3 is one of its factors.

[A] b x + 3 gb x − 2 gb 2 x − 1 g [B]b x + 3 gb x − 2 gb 2 x + 1 g

[C] b x + 3 gb x + 2 gb 2 x − 1 g [D]b x + 3 gb x + 2 gb 2 x + 1 g

_____ 29. Find the vertical asymptote(s), if any, for f x x

b g x x

[A] (^) x = 7 , x = 3 , x =– 4 [B] x = – 4 , x = 7

[C] (^) x = 7, x = 3 [D] No vertical asymptotes

_____30. A biologist took a count of the number of migrating waterfowl at a particular lake, and re-counted the lake’s population of waterfowl on each of the next six weeks. Find a quadratic function that models the data shown as a function of the number of weeks, x. Week 0 1 2 3 4 5 6 Population 762 618 558 582 690 882 1158

[A] P x b g = 41 x^2 – 179 x + 756 [B]

P x b g = 44 x^2 – 198 x + 762

[C] P x b g = 42 x^2 – 186 x 762 [D] P x b g = 45 x^2 – 198 x + 756

Find the graph of the function.

_____31. f b g x = 3 x – 5

[A]

−10 10

−

[B]

−10 10

−

_____34. Evaluate the expression without using a calculator. ln 3 e

[A] 1

[B] 1

3 e

[C] (^3) e [D] 3

_____35. Find a graph that models an exponential growth function.

[A]

–10 10

[B]

–10 10

[C]

–10 10

[D]

–10 10

_____36. Solve the system of linear equations 8 6 5 3 4 64 3 4 36

x y z x y z x y z

36 MCQs for Final Examination - College Algebra | MAT 110, Exams of Algebra

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Partial preview of the text

Download 36 MCQs for Final Examination - College Algebra | MAT 110 and more Exams Algebra in PDF only on Docsity!

[B]

[C]

[B]

[C]

[D]

[A]

[B]

[C]

[D]

_____9. f b g x = x + 1; f b g 5

[A] 6 [B] 4 [C] –4 [D] –

_____10. f b g x = 2 x^2 − 4 x ; f b g 3

[A] 11.072 [B] 14.536 [C] 12 [D] 6

b g x x

= +^ +

_____12. f b g x = − 3 x + 1

[A] (a) C x b g = 5 75 29 00. +.

[B] (a) C x b g = 29 00. x +5 75.

[C] (a) C x b g = 5 75. x +29 00.

[D] (a) C x b g = 5 75. x

y = − b x − 3 g 2 + 1

[A] Increasing on b 3 , ∞ g; Decreasing on b− ∞, 3 g

[B] Increasing on b – 1 , ∞ g; Decreasing on b− ∞, – 1 g

[C] Increasing on b − ∞, 3 g; Decreasing on b 3 ,∞g

[D] Increasing on b 1 , ∞ g; Decreasing on b− ∞, 1 g

[C]

[D]

g x b g b = x + 2 g^2 + 4

[A] a horizontal shift of f b g x = x^2 two units to the right and a vertical shift of y 4 units upward

f b g x = x^2

[C] a horizontal shift of f b g x = x^2 two units to the left and a vertical shift of y 4 units downward

[D] a horizontal shift of f b g x = x^2 two units to the left and a vertical shift of y 4 units upward

_____19. Find b f + g gb g x and b f + g gb 3 gfor and

f b g x = 5 x^2 + x + 5 g x b g = − 2 − 5 x + 3 x 2.

F x

HG^

I

KJb g^

for f b g x = 4 − x^2 and g x b g = 2 − x.

_____ 21. If f b g x = 2 − x and g x b g = 3 x + 4 , find (a) b f D g gb x g and (b)b g D f gb x g.

f b g x = 2 x +^1

g x b g = 1 x −

[A] Yes [B] No; g x b g = 2 x −

[C] No; g x b g = 3 x +

[D] No; g x b g = 1 x +

_____ 23. f b g x = 3 x − 1

[A] f −^1 b g x = x − 1 [B] f −^1 x = 1 x −

b g

b g D]^ f^ −^1 b g x^ =^ x +^1

f b g b x = x − 4 g^2 − 1

[A] Upward; b 4 , – 1 g [B] Upward;b – 4 , 1 g

[C] Downward; b 4 , – 1 g [D] Downward;b– 4 , 1 g

f b g x = x^2 − 4 x + 2

[A]

[B]

No x - intercepts d 2 + 2 , 0 ,i d 2 − 2 , 0i

[C]

[D]

d 2 +^2 , 0 ,i d^2 −^2 , 0i b^ −^3 , 0 ,^ g b^ −^1 , 0g

f b g x = − 6 x^4 + 150 x^2

[A] b x + 3 gb x − 2 gb 2 x − 1 g [B]b x + 3 gb x − 2 gb 2 x + 1 g

[C] b x + 3 gb x + 2 gb 2 x − 1 g [D]b x + 3 gb x + 2 gb 2 x + 1 g

b g x x

[A] P x b g = 41 x^2 – 179 x + 756 [B]

P x b g = 44 x^2 – 198 x + 762

[C] P x b g = 42 x^2 – 186 x 762 [D] P x b g = 45 x^2 – 198 x + 756

_____31. f b g x = 3 x – 5

[A]

[B]

[A] 1

[B] 1

[B]

[C]

[D]

R

S