Precalculus

MATH 115 Precalculus Fall, 2015, V3.2
Page 3 of 7
6. Which of the functions corresponds to the graph? 6. ______
A. f (x) = 2 + cos x
B. f (x) = 2(1 – cos x)
C. f (x) = 3 – cos x
D. f (x) = 2 – sin x
SHORT ANSWER:
7. Points (8, –1) and (6, –5) 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. Amanda, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 2.7% of her
annual income. If Amanda paid $1,535 in tax, what was Amanda’s income?
Answer: _____________
MATH 115 Precalculus Fall, 2015, V3.2
Page 4 of 7
10. A bowl of soup at 185° F. is placed in a room of constant temperature of 75° F. The
temperature T of the soup t minutes after it is placed in the room is given by
T(t) = 75 + 110 e
– 0.075 t
Find the temperature of the soup 24 minutes after it is placed in the room. (Round to the nearest
degree.)
Answer: ________
11. Given the function

=19
-13
, find a formula for the inverse function.
Answer: __________________
12. (a) State the reference angle associated with 300°. Answer: ________
(b) Convert 300° to radians. Leave the answer in terms of p. Answer: ________
13. Given y = 3 sin(8x – p), state the
(a) period Answer: ________
(b) phase shift Answer: ________
14. Solve the trigonometric equation (cos x)(2sin x – 1) = 0 in the interval [0, 360°).
Answer: _________________
15. (a) Find the exact value of arcsin sin 
 Answer: ________
(b) Find the exact value of arccos sin 

Answer: ________
16. For the parabola given by (x – 4)2 = –8(y + 3), find the following:
(a) direction parabola opens (to the left, right, up, or down) Answer: ___________
(b) vertex Answer: ___________
(c) focus Answer: ___________
MATH 115 Precalculus Fall, 2015, V3.2
Page 5 of 7
17. Let
3 1
( )
2
x
f x
x
+
=
–
.
(a) State the domain. Answer: _________________
(b) State the horizontal asymptote. Answer: _________________
(c) State the vertical asymptote(s). Answer: _________________
(d) Which of the following represents the graph of
3 1
( )
2
x
f x
x
+
=
–
? Answer: ______________
GRAPH A. GRAPH B.
GRAPH C. GRAPH D.
MATH 115 Precalculus Fall, 2015, V3.2
Page 6 of 7
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, 7). Write the
equation in slope-intercept form. Show work.
19. Find the exact solutions and simplify as much as possible: 7×2 – 2 = 2x. Show work.
20. Let f (x) = 5×2 + 7 and g(x) = x – 2.
(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 8 feet high with an initial velocity of 112 feet per second,
The height h of the projectile at t seconds after launch is given by h = –16t2 + 112t + 8 feet.
(a) How many seconds after launch does the projectile attain maximum height? Show work.
(b) What is the maximum height? Show work.
22. Solve:
2
11 56

4 16
x
x x
+
+ =
+ –
. Show work.
23. Suppose that cos q = 5/13 and that q is a Quadrant IV angle.
(a) Find the exact value of sin q. Show work.
(b) Find the exact value of sin 2q. Show work.
24. Prove the identity (sin x + cos x)2 – 1= sin 2x
MATH 115 Precalculus Fall, 2015, V3.2
Page 7 of 7
25. From a point 63 feet from the base of a redwood tree, the angle of elevation to the top of the
tree is 51.8°. Find the height of the tree to the nearest 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 b rounded to the nearest hundredth. Show work.
27. Let  = 4, 6 and  = 12, –8.
(b) Calculate the dot product  · . Show work.
(c) Determine the angle between  and . Round the result to the nearest degree. Show work.
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.