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PreCalc BC Final Review Semester 1

Total questions: 74

Worksheet time: 3hrs 27mins

Name
Class
Date
1.
What kind of asymptotes do logs have?
a)
horizontal ( y=0)
b)
vertical (x=0)
2.
Find the domain and range of:
f(x) = ln(x)
a)
D: all real numbers
R: y > 0
b)
Domain: all real numbers
Range: all real numbers
c)
Domain: x > 0
Range: all real numbers
d)
Domain: all real numbers
Range: y < 0
3.
State the domain restrictions.
a)
x ≠ 3, -2, 6, -1
b)
x ≠ -1, 6
c)
x ≠ 3, -2
d)
No Domain Restrictions
4.

Identify the Range

a)

(- ∞, -2 ]

b)

[ -2, ∞ )

c)

All Real Numbers

d)

[ 0, ∞)

5.
Find the domain and range of the function
Hint:  Use a scratch graph to help you visualize things. 
a)
Domain: (-∞, ∞)  Range: [-∞, 4]
b)
Domain: [1, ∞)  Range: (-∞, 4]
c)
Domain: [-1. ∞) Range: [4, ∞) 
d)
Domain: [4, ∞) Range: [-1,∞) 
6.
What are the transformations of this functions compared to the parent function?
a)
Shifted right 5, shifted down 2, and reflected over the x-axis
b)
Reflected over the x-axis, vertical stretch, and shifted right 5
c)
Reflected over the x-axis, vertical stretch, and shifted left 5
d)
Shifted right 5, shifted down 2
7.
#7 - List the types of intervals that the graph demonstrates in order.
a)
decreasing, constant, increasing, constant
b)
increasing, decreasing, constant
c)
increasing, constant, increasing, constant
d)
increasing, constant, decreasing, constant
8.
What are the local maxima of this graph?
a)
local maximum at (2.2, 3.9)
b)
local maximum at (-8, 5)
c)
local maximum at (5, -8)⋃(3.9, 2.2)
d)
local maximum at (-8, 5)⋃(2.2, 3.9)
9.
How did we transform from the parent function?
y = -1/2(x - 1)2 + 3
a)
reflection, vertical compression, horizontal right, vertical up
b)
vertical compression, horizontal shift left, vertical shift up
c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
10.
What is the range of
y= -3sin(x)-2?
a)
[-2,2]
b)
[-5,1]
c)
[-4,2]
d)
[-3,3]
11.
What is the period?
a)
4π
b)
2π
c)
π
d)
8π
12.
What is the period of y=4cos5x
a)
2π/5
b)
π
c)
5
d)
5π
13.
what is the amplitude of y=3sin(7x)-2
a)
7
b)
-2
c)
3
d)
6
14.
Which trig function does this graph represent?
a)
csc
b)
sec
c)
tan
d)
cot
15.
a)

a

b)

b

c)

c

d)

d

16.
a)
b)
c)
d)
17.
a)
b)
c)
d)
18.
a)
b)
c)
d)
19.
a)
b)
c)
d)
20.
What is the horizontal asymptote? 
a)
x = 2
b)
x = 7
c)
y = 2
d)
y = 7
21.

Which is the graph of the rational equation:

a)
b)
c)
d)
22.

What is the domain of this function?

a)

All real numbers except -4

b)

All real numbers except -3

c)

All real numbers except 3

d)

All real numbers except 0

23.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

24.

What is the Range of this function?

a)

All real numbers except 5

b)

All real numbers except 6

c)

All real numbers except 0

d)

All real numbers except 2

25.
What is the vertex of the function
f(x) = -x2+8x-10?
a)
(4,6)
b)
(4,38)
c)
(-4, -10)
d)
(8, -10)
26.
Does the equation have a max or min?
y = 2x2 + 7x + 5
a)
max
b)
min
27.

What is the order, from narrowest to widest graph, of the quadratic functions f(x) = -10x2, f(x) = 2x2, and f(x) = 0.5x2?

a)

f(x) = -10x2 , f(x) = 2x2, and f(x) = 0.5x2

b)

f(x) = 2x2, f(x) = -10x2, and f(x) = 0.5x2

c)

f(x) = 0.5x2, f(x) = 2x2, and f(x) = -10x2

d)

f(x) = 0.5x2, f(x) = -10x2, and f(x) = 2x2

28.

Which expression gives the solutions of -5 + 2x2 = -6x?

a)
b)
c)
d)
29.
7.  What is the phase shift for y = 4cos(1/2x +π) - 2?
a)
left pi/2
b)
right pi/2
c)
right 2pi
d)
left 2pi
30.
13.  What is the equation of the graph?
a)
y = -2 cos x - 3
b)
y = 3 cos x - 2
c)
y = -7 cos x - 3
d)
y = -3 cos x - 4 
31.
1.  Find the Exact Value
a)
A
b)
B
c)
C
d)
D
32.
2.  Find The Exact Value
a)
A
b)
B
c)
C
d)
D
33.
4.  Which of the following is True?
a)
x +, y +
b)
x -, y -
c)
x -, y +
d)
x +, y -
34.
6.  Name That Quadrant
a)
I
b)
II
c)
III
d)
IV
35.
7.  Find the Exact Value
a)
A
b)
B
c)
C
d)
D
36.
Find the arc length of the bolded arc.
a)
A
b)
B
c)
C
d)
D
37.
Convert to radians: 15°.
a)
π/18
b)
π/12
c)
π/6
d)
19π/90
38.
When f(x) = 2x and g(x) = x2+3 , find f(g(x)).
a)
x2+2x+3
b)
4x2+3
c)
2x2+3
d)
2x2+6
39.
Which graph matches the equation?
a)
A
b)
B
c)
C
d)
D
40.
a)
A
b)
B
c)
C
d)
D
41.
Pick the equation that matches the graph
a)
A
b)
B
c)
C
d)
D
42.
Given -4 is a zero, find all other zeros
f(x) = x3+4x2+9x+36
a)
x = -2, 2
b)
x = -3, 3
c)
x =  -2i, 2i
d)
x = -3i, 3i
43.
Find the inverse
a)
A
b)
B
c)
C
d)
D
44.
Find ALL Asymptotes
a)
A
b)
B
c)
C
d)
D
45.
Which of the following is false?
a)
A
b)
B
c)
C
d)
D
46.

Even, Odd, or Neither?

a)

Even

b)

Odd

c)

Neither

d)

Please explain this to me.

47.
a)

Even

b)

Odd

c)

Neither

48.

Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical compression by a factor of 3

d)

horizontal shift to the left 2 and vertical compression by a factor of 3

49.

When is this function increasing?

a)

{x| -2.5 ≤ x ≤ 2.5}

b)

{x| 0 ≤x ≤ 5}

c)

{x| 0 ≤ x ≤ 55}

d)

{x| -5 ≤ x ≤ 0}

50.
Determine the average rate of change over the interval [-2, 2].
a)
4
b)
-4
c)
1
d)
-1
51.

Which of the following intervals has the largest average rate of change?

a)

[13,14]

b)

[13, 17]

c)

[16, 17]

d)

[16, 19]

52.

Use your graphing calculator to find the zeros for

-x2+3x+2=0

a)

-3.562 and -0.562

b)

3.562 and -0.562

c)

-3.562 and 0.562

d)

3.562 and 0.562

53.
What is g(7) if:
a)
-17
b)
-13 
c)
13       
d)
17
54.

What is the Equation?

a)

A

b)

B

c)

C

d)

D

55.

If a lawyer charges $120 an hour (or any fraction of an hour, or in other words, you use one minute of the next hour, you pay for the whole hour), how much is a bill for 3 hours and 20 minutes?

a)

$420

b)

$480

c)

$400

d)

$360

56.

What is the DOMAIN

Given f(x) = 3x2+1 and g(x) = -2x-3

of (f/g) (x)

a)

ℝ, x ≠ -3/2

b)

ℝ, x ≠ 3/2

c)

ℝ, x > -3/2

d)

ℝ, x > 3/2

57.

What is the domain of the function?

a)

ℝ, x ≠ 2, -2

b)

ℝ, - 2 < x < 2

c)

ℝ, - 2 ≤ x ≤ 2

d)

x < 2

58.
What is f when x equals 4?
a)
-5
b)
0
c)
3
d)
6
59.

What's another word for 'x-intercept'? Check ALL that apply.

a)

root

b)

solution

c)

zero

60.
Find the inverse of f(x) = -4x - 12
a)
f-1(x) = 4x - 3
b)
f-1(x) = -1/4x - 3
c)
f-1(x) = 1/4x + 3
d)
f-1(x) = -4x - 3
61.
a)
Even Degree
- Leading Coeff.
b)
Even Degree
+ Leading Coeff.
c)
Odd Degree
- Leading Coeff.
d)
Odd Degree
+ Leading Coeff.
62.
Which equation MOST LIKELY matches the graph?
a)
y = x4 - x3 + 3x2 + 2
b)
y = -x4 + x3 + 5x + 2
c)
y = x3 - 2x2 + 1x + 3
d)
y = -x3 - 2x2 + 1x + 3
63.

Even Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis

b)

Touches the x-axis

64.

Please select the solution that describes if zeros crosses or turns at the x-axis for each x-intercept.

a)

2 crosses, 1 crosses, -3 touches, -4 touches

b)

1 crosses, -3 touches , - 4 crosses

c)

1 crosses, -3 touches , -4 touches

d)

1 touches , -3 crosses, -4 crosses

65.
4. Solve
7x+10-8=6
a)
-7.374
b)
-8.643
c)
-7.360
d)
-8.853
66.
6. log2(x + 5) = 3
a)
3
b)
4
c)
5
d)
6
67.
Which graph represents an exponential function?
a)
f(x)
b)
g(x)
c)
h(x)
d)
k(x)
68.
Are these inverse functions
a)
no
b)
yes
c)
no way to tell
69.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

70.
Find the oblique asymptote.
a)
y = 3x - 12
b)
y = x + 5
c)
y = 3x - 5
d)
y = 3x - 7
71.
Use the exponential regression to find an equation that fits the​ data, where x is the years since 1990.
a)
y=8.92•1.23x
b)
y=1.23•8.92x
c)
y=8.92+1.23x
d)
y=8.92x+1.23
72.

The maximum number of organisms an area can support is called

a)

limiting factors

b)

survival rate

c)

maximum space

d)

carrying capacity

73.
What is the carrying capacity of the following graph?
a)
1000
b)
8000
c)
800
d)
600
74.
The data table in the picture shows the average length of daylight for each month of the year.  Calculate the sinusoidal regression equation of the data.
a)
y = 2.69sin(0.512x - 1.47) + 11.89
b)
y = 11.89sin(2.69x + 0.512) - 1.47
c)
y = -0.106x + 12.44
d)
y = 12.44x - 0.106

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