Download Math 143 Final Review (15 pages reduced 4 pages by cutting out

Math 143 Final Review
(15 pages reduced 4 pages by cutting out many
multiple choice answers.)
1. Find the domain of the following function:
x  10
f(x) = 2
x 4
Name________________________________
7. Which of the following pairs of functions can be
x3
used in f ◦ g to create: G(x) = 3
?
x 2
2. Sketch the graph of the piecewise defined
function.
8. An airplane is flying at a speed of 250 mph at an
altitude of 4 miles. The plane passes directly above
a radar station at time t = 0. Find the distance s
between the plane and the radar station after 4 min.
3. Determine whether the equation defines y as a
function of x: x2 + 3y = 3
Yes or No
a. 17.6 mi b. 17.1 mi c. 16.6 mi
d. 18.1 mi e. 19.0 mi
4. Determine the interval on which the function in
the graph below is decreasing.
a. [4, –1] b. [–2, 7] c. [–3, 6]
d. [–7, –3] e. [6, 10]
5. Find the max or min value of y = –x2 + 8x.
a. min = 16 b. max = 24 c. min = –32
d. min = –16 e. max = 16
6. Using transformations, explain how the graph of
g is obtained from the graph of f.
f(x) = x ,
g(x) = ½ x  5
11. A one-to-one function is given. Find the inverse.
Were you to graph both, what transformation is here
f(x) = 1 – ¼ x
12. Given the function y = x2 – 4x + 3.
Find the coordinates of its vertex and its intercepts.
13. Find the vertex of y = 6x2 + 12x – 11
x2 1
x9
a. x = –9 b. x = –1 c. x = 18 d. x = 1 e. x = 9
20. Find the vertical asymptote of r ( x) 
14. Write in vertex form and find the min or max
value of f(x) = 9 – 8x – 8x2
15. If a ball is thrown directly upward with a
velocity of 80 ft/s, its height (in feet) after t seconds
is given by y = 80t – 16t2 .
What is the maximum height attained by the ball?
a. 25 ft b. 176 ft c. 50 ft d. 100 ft e. 80 ft
16. Determine the end behavior of the graph of:
y = 8x3 – 7x2 + 3x + 7
17. Find the quotient and remainder using synthetic
2x 4  7 x3  9x 2  7 x  8
division.
1
x
2
21. Find the y-intercept and both asymptotes of
75
r ( x) 
( x  5) 2
a. (0, 3), y = 5, x = 0 b. (0, 5), y = 0, x = 3
c. (0, 3), y = 0, x = 5 d. (0, 3), y = 1, x = –5
e. (0, 5), y = 1, x = 3
22. Find the domain of f ( x) 
1
1 x
a. (–∞, ∞) b. (1, ∞) c. (–∞, 1)
d. [1, ∞) e. (–1, 1)
23. Given the graph, find the sum of the roots.
18. Find all rational zeros of the polynomial:
P(x) = x3 + 3x2 – 4
a. 1, 2 b. –1, –2 c. 1, –2 d. 1, –1 e. 1, –½
a. –5 b. 3 c. –3 d. 2 e. –2
24. Find the rule for the function below.
19. Find all rational zeros of the polynomial
P(x) = x4 + 11x3 + 29x2 – 11x – 30
a. –1, –5, –6 b. –1, 1, –5, 6 c. 1, 3, –5, –6
d. –1, 1, 5, –6 e. –1, 1, –5, –6
a. f(x) = –x3 + 3x – 6
c. f(x) = x4 – 3x2 – 6
e. f(x) = x4 – 3x2 + 6
b. f(x) = –x4 – 3x2 – 6
d. f(x) = x5 – 3x2 – 6
25. Express ln(x + 1) = 4 in exponential form.
32. Find the exact values of the trigonometric
13
7
functions sec
and csc
3
3
26. Express 34 = 81 in logarithmic form.
27. Evaluate the expression: log3 189 – log3 7
a. 21 b. ln 189 c. 7 d. 3 e. log3 182
28. Use the Laws of Logarithms to rewrite the
expression below in a form with no logarithm of a
product, quotient, or power.
log
x2  6
( x 2  1)( x 5  4) 2
33. Find the values of the trigonometric functions of
11
t if tan t = 
and cos t > 0.
5
34. Find the values of the trigonometric functions of
6
t if cos t = 
and the terminal point of t in QIII.
10
35. Sketch the graph of y = 5 cos
1
x
3
29. Solve the logarithmic equation for x.
log2 2 + log2 x = log2 3 + log2 (x – 5)
a. x = 12 b. x = 30 c. x = 15
d. x = 17 e. x = 3.9
30. Solve the logarithmic equation for x.
log5 (x + 3) – log5 (x – 3) = 2
a. x = 6.5 b. x = 2 c. x = 2.77
d. x = 0.31 e. x = 3.25
31. Find the time required for an investment of
$3,000 to grow to $8,000 at an interest ratte of 8%
per year.
a. 13 yrs b. none c. 12 yrs d. 50 yrs e. 3 yrs
36. Each time your heart beats, your blood pressure
increases, then decreases as the heart rests between
beats. A certain person’s blood pressure is modeled
by the function. p(t) = 90 + 20 sin (160π t). Find the
amplitude, period and frequency.
37. Find sin α and cos β if x = 4 and y = 1.
38. The angle of elevation to the top of a particular
skyscraper in New York is found to be 12° from the
ground at a distance of 1.3 mi from the base of the
building. Using this information, find the height of
the skyscraper.
a. 1560 ft b. 2918 ft c. 1459 ft
39. A man is lying on the beach, flying a kite. He
holds the end of the kite string at ground level, and
estimates the angle of elevation of the kite to be
55°. If the string is 470 ft long, how high is the kite
above the ground?
a. 470 ft b. 574 ft c. 385 ft
43. If sin x = c and x is in the first quadrant,
find sin (2x) in terms of c.
a. 2c (1 – c)2
b. 2c2 1  c 2
d. 2c 1  c 2
e. 2c 1  c 2
c. 2 1  c 2
44. Simplify as much as possible:
1  cos x
sin x

sin x
1  cos x
a. 2 sin x b. cos x c. sin x d. 2 csc x
45. A 78 ft tree casts a shadow that is 100 ft long.
What is the angle of elevation of the sun?
a. 46.57° b. 14.15° c. 34.62° d. 11.85° e. none
40. Find the area of the shaded region if r = 6
and θ = 129°.
a. 81.442
b. 54.515
c. 26.538
d. none
41. Find all solutions of the following equation:
sin2 x = –3 sin x + 4
42. Find all solutions of the following equation.
cos x (2 sin x + 2 ) = 0