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[answered] MATH 115 Precalculus Fall, 2016, V4.3 MATH 115 FINAL EXAMIN


Pre calculus assignment. Questions are on a PDF attachment and there is a separate answer sheet that is attached that should be filled out.


MATH 115 Precalculus Fall, 2016, V4.3 MATH 115 FINAL EXAMINATION

 

This is an open-book exam. You may refer to your text and other course materials as you work

 

on the exam, and you may use a calculator. You must complete the exam individually.

 

Neither collaboration nor consultation with others is allowed.

 

Record your answers and work on the separate answer sheet provided.

 

There are 28 problems.

 

Problems #1?6 are Multiple Choice.

 

Problems #7?17 are Short Answer. (Work not required to be shown)

 

Problems #18?28 are Short Answer with work required to be shown.

 

MULTIPLE CHOICE

 

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

 

A.

 

B.

 

C.

 

D. 1. ______ (??, ?9/4] ? [3, ?)

 

(??, ?9/4]

 

[?9/4, 3]

 

[?9/4, ?) 2. Which of the following polynomials has a graph which exhibits the end behavior of

 

downward to the left and downward to the right?

 

2. _______ A.

 

B.

 

C.

 

D. f (x) = ?6x5 ? x3 ? x2 ? 5

 

f (x) = 8x3 + 6x2 ? x + 3

 

f (x) = 5x6 + 7x2 + x

 

f (x) = ?3x4 + 9x2 ? x ? 1 vvvv 3. Express as an equivalent expression: 8 log y + log 1 ? log (x ? 3)

 

A. y8 log x ?3 B. log(8 y )

 

log( x ? 3) C. 8y +1

 

log x ?3 D. log ( 8 y + 4 ? x ) 3. ________ Page 1 of 7 MATH 115 Precalculus

 

4. Determine the interval(s) on which the function is increasing. A. ( ? 4 / 3, 1) B. ( ?1,1) and ( 3, ? ) C. ( ??, ?5 / 3) , ( 0, 2 ) , and (11/ 3, ? ) D. ( ??, 0 ) and ( 2, ? ) 5. Which of the functions corresponds to the graph? Fall, 2016, V4.3

 

4. ______ 5. ______ A. f ( x ) = e x ? 1

 

B. f ( x ) = ?e x + 1

 

C. f ( x ) = ?e x

 

D. f ( x ) = e? x + 1 Page 2 of 7 MATH 115 Precalculus Fall, 2016, V4.3 6. Which of the functions corresponds to the graph? 6. ______ A. f (x) = cos(2x) + 2

 

B. f (x) = 3 ? sin x

 

C. f (x) = sin x + 3

 

D. f (x) = 2 cos x + 1 SHORT ANSWER:

 

7. Points (?7, 2) and (5, 6) are endpoints of the diameter of a circle.

 

(a) What is the exact length of the diameter? (Simplify as much as possible) Answer: ________ (b) What is the center of the circle? Answer: ____________ (c) What is the equation of the circle? Answer: ___________________________ 8. Find the value of the logarithm: log?? ? ? ??? ?. Answer: ____________ 9. Bill, a resident of Metropolis, pays Metropolis an annual tax of $55 plus 1.8% of his annual

 

income. If Bill paid $1,441 in tax, what was Bill?s income?

 

Answer: _____________ Page 3 of 7 MATH 115 Precalculus Fall, 2016, V4.3 10. A can of soda at 71? F. is placed in a refrigerator that maintains a constant temperature of 39?

 

F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t) = 39 + 32 e ? 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: ________

 

1 11. Given the function ?????? = 3 ? ???, find a formula for the inverse function.

 

8

 

Answer: __________________ 12. (a) State the reference angle associated with 300?. Answer: ________ (b) Convert 300? to radians. Leave the answer in terms of ?. Answer: ________ 13. Given y = 9 sin(8x ? ?), state the

 

(a) period Answer: ________ (b) phase shift Answer: ________ 14. Solve the trigonometric equation (cos x)(2cos x + 1) = 0 in the interval [0, 360?).

 

Answer: _________________ 15. (a) Find the exact value of arccos ?sin (b) Find the exact value of arcsin ?tan ??

 

? ??

 

? ? Answer: ________ ? Answer: ________ 2 16. For the parabola given by (y + 5) = 8(x ? 2), find the following:

 

(a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________

 

Page 4 of 7 MATH 115 Precalculus

 

17. Let f ( x) = Fall, 2016, V4.3 3x + 1

 

.

 

x?2 (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) = 3x + 1

 

?

 

x?2 GRAPH A. GRAPH B. GRAPH C. GRAPH D. Answer: ______________ Page 5 of 7 MATH 115 Precalculus Fall, 2016, V4.3 SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (1, ?1) and (3, ?9). Write the

 

equation in slope-intercept form. Show work. 2 19. Find the exact solutions and simplify as much as possible: 5x = 1 + 6x. Show work. 2 20. Let f (x) = 5x ? 9 and g(x) = x ? 4.

 

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

 

(b) Find ( f o g )(?1) . Show work. 21. A projectile is launched from a platform 15 feet high with an initial velocity of 48 feet per second.

 

The height h of the projectile at t seconds after launch is given by h = ?16t2 + 48t + 15 feet. (a) How many seconds after launch does the projectile attain maximum height?

 

(b) What is the maximum height? 22. Solve: Show work. Show work. x?6

 

16

 

+ 2

 

= 0 . Show work.

 

x ? 4 x ? 16 23. Suppose that cos ? = 5/13 and that ? is a Quadrant IV angle.

 

(a) Find the exact value of sin ?. Show work. (b) Find the exact value of sin(2? ). Show work. 2 24. Prove the identity (sin x + cos x) ? sin(2x) = 1 Page 6 of 7 MATH 115 Precalculus Fall, 2016, V4.3 25. From a point 48 feet from the base of a redwood tree, the angle of elevation to the top of the

 

tree is 52.3?. Find the height of the tree to the nearest tenth of a foot. Show work.

 

(sketch is not to scale) 26. For the triangle ABC, we are given that A = 46?, B = 64?, and c = 35.0. Find the length of side a, rounded to the nearest tenth. Show work. ?? = ?10, ?5? and ?

 

?? = ?2, 4?.

 

27. Let ?

 

(b) ?? ? ?

 

??. Show work.

 

Calculate the dot product ? (c) ?? and ?

 

??. Round the result to the nearest degree. Show work.

 

Determine the angle between ? 28. An ellipse has the equation ?? ? ???

 

?? + ?? ? ???

 

? =1 (a) Is the major axis horizontal or vertical?

 

(b) Find the exact values of the foci of the ellipse. Show work.

 

Page 7 of 7

 


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