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Functions PreCalc BC Honors

Total questions: 55

Worksheet time: 2hrs 7mins

Name
Class
Date
1.

Is this a function?

a)

Function

b)

Not a Function

2.

Is this a function?

a)

Function

b)

Not a Function

3.
Is this set of ordered pairs a function or not a function? 
a)
Function
b)
Not a Function 
4.

Even, Odd, or Neither?

a)

Even

b)

Odd

c)

Neither

d)

Please explain this to me.

5.
a)

Even

b)

Odd

c)

Neither

6.
a)

Even

b)

Odd

c)

Neither

7.
Is the graph an even, odd, or neither function 
f(x)=x3-x2
a)
even
b)
odd
c)
neither
8.

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

9.
To what is the graph of an odd function symmetric?
a)
x-axis
b)
y-axis
c)
the line y=x
d)
origin
10.
  The blue function is the parent function f(x) = x3.  Which of the following is the correct equation for the red function, g(x)?
a)
g(x)=x3+1
b)
g(x)=x3-1
c)
g(x)=(x-1)3
d)
g(x)=(x+1)3
11.
Is the graph an even, odd, or neither function
                        f(x) = (x+4)2 - 1
a)
Even
b)
Odd
c)
Neither
12.
Is the graph an even, odd, or neither function
                        f(x) = x2 + 2
a)
Even 
b)
Odd
c)
Neither
13.
Which of the following is false?
a)
A
b)
B
c)
C
d)
D
14.
Which of the following transformations are present?
-2f(x - 1) + 2
a)
Shift 1 unit down
b)
Shift 1 unit up
c)
Shift 1 unit left
d)
Shift 1 unit right
15.
Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5
a)
Shifted up 5 units
Shifted right 3 units
Stretched vertically by a factor of 3
b)
Shifted up 5 units
Shifted left 3 units
Stretched vertically by a factor of 3
c)
Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 3
d)
Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 1/3
16.

f(x) = 4 - x2

a)

Reflect over x-axis

Up 4

b)

Reflect over x-axis

Down 4

c)

Reflect over y-axis

Up 4

d)

Reflect over y-axis

Down 4

17.

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}

18.

Where is the function increasing?

a)

[4, ∞)

b)

[−4, ∞)

c)

[6, ∞)

d)

4 < x < 6

19.
Determine the average rate of change over the interval [-2, 2].
a)
4
b)
-4
c)
1
d)
-1
20.

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

a)

[13,14]

b)

[13, 17]

c)

[16, 17]

d)

[16, 19]

21.
f(x) = 2x2 + 12x + 16
What is the average rate of change of f(x) on the interval [-3, -2].
a)
2
b)
1/2
c)
-2
d)
-1/2
22.
What is g(7) if:
a)
-17
b)
-13 
c)
13       
d)
17
23.

What is the Domain?

a)

A

b)

B

c)

C

d)

D

24.

What is the Equation?

a)

A

b)

B

c)

C

d)

D

25.

What is the Range?

a)

A

b)

B

c)

C

d)

D

26.

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

27.
The flag belongs to...
a)
Algeria
b)
Kirghizstan
c)
Papua new Giunea
d)
Trynidad and Tobago
28.
The flag belongs to...
a)
Ughanda
b)
Qatar
c)
Cuba
d)
Belize
29.
The flag belongs to...
a)
Republic of Lithuania
b)
Nepal
c)
Republic of Mali
d)
Kenya
30.
If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?
a)
7
b)
-2
c)
-9
d)
-10
31.
Given
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f + g)(x).
a)
11x2 - 1
b)
5x4 + 6x2 - 1
c)
5x2 + 6x - 1
d)
5x2 + 8x - 1
32.
f(x) = 3x2 + 7x and g(x) = 2x2 - x - 1, find (f - g)(x).
a)
x2 + 8x + 1
b)
x2 + 6x - 1
c)
5x2 + 8x - 1
d)
x2 + 8x -1
33.
Given f(x) = 3x2 - 2x + 1 and g(x) = x - 4, find (f⋅g)(x). 
a)
3x3 - 10x2 - 7x - 4
b)
3x3 - 14x2 + 9x - 4
c)
3x2 - x - 3
d)
3x3 + 14x2 - 9x - 4
34.

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

Find f(x-h)

a)

3x2 - 6xh + 3h2 + 1

b)

3x2 - 3h2 + 1

c)

3x2 - 6xh + 3h2

d)

3x2 + 3h2 + 1

35.

Given f(x) = 3x2 - 2x + 1 and g(x) = x - 4, find (f - g)(x)

a)

3x2 - x + 3

b)

3x2 - 3x + 3

c)

3x2 -3x + 5

d)

-2x2 - x + 3

36.

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

37.

What is the domain of the function?

a)

ℝ

b)

ℝ, x ≠ ±1

c)

ℝ, x ≠ 1

d)

ℝ, x > ±1

38.

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

39.

In what year was Netflix founded?

a)

1997

b)

2007

c)

2010

d)

2013

40.

In what year was Facebook created?

a)

2001

b)

2004

c)

2007

d)

2009

41.

What year was Coca Cola created?

a)

1872

b)

1892

c)

1912

d)

1932

42.

Write an equation for the function whose graph of y = x3, but is:

Shifted up 3

Shifted left 5

a)

(x - 5)3 + 3

b)

(x + 5)3 - 3

c)

(x - 5)3 - 3

d)

(x + 5)3 + 3

43.

At 8 am, the depth of the snow outside is 3 in. At noon, the depth has increased to 11 in. What is the average rate of change of the depth of the snow from 8 am to noon?

a)

1/2 inches per hour

b)

8 inches per hour

c)

2 inches per hour

d)

4 inches per hour

44.
What is f when x equals 4?
a)
-5
b)
0
c)
3
d)
6
45.
What is m(-3) if:    
a)
-3
b)
0.5
c)
3
d)
-3.5
46.
On the graph, which portion of the piecewise function is represented in red?
a)
x
b)
0.5x + 2.5       
c)
-1
d)
0.5x + 2
47.
Using the pictured graph, what is f(-3)? 
a)
-3
b)
-1
c)
1
d)
3
48.
Where is this piecewise function discontinuous and what type of discontinuity is it?
a)
x =2 point
b)
x = 2 jump
c)
x = -1 point
d)
x = -1 jump
49.

What is f(-12)?

a)

7

b)

204

c)

-48

d)

-84

50.
What are the transformations of this functions compared to the parent function y = √(x)?
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
51.
What are the transformations to the graph compared to the parent function y=√(x)?
a)
Shifted right 2, shifted up 3, and reflected over the y-axis
b)
Shifted left 2, shifted up 3, and reflected over the y-axis
c)
Shifted left 2, shifted up 3, and reflected over the x-axis
d)
Shifted right 2, shifted up 3, and reflected over the x-axis
52.
Describe the transformation of y = f(x) for the new function
f(x) = ⅔(x - 7)2 
a)

Compress Vertically by ⅔
Right 7

b)

Compress Vertically by ⅔
Left 7

c)

Compress Horizontally by ⅔
Right 7

d)

Compress Horizontally by ⅔
Left 7

53.
If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?
a)
-f(x)
b)
f(-x)
c)
f-1(x)
d)
f(2x)
54.
Describe the transformation of y = f(x) to the new function
 y = f(1/5x)
a)
Horizontal shrink by a factor of 1/5
b)
Vertical stretch be a factor of 5
c)
Vertically shrink by a factor of 1/5
d)
 Horizontal stretch by a factor of 5
55.
Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10
a)
Reflect over y-axis
Shifted down 10 units
Shifted left 6 units
b)
Reflect over x-axis
Shifted up 10 units
Shifted left 6 units
c)
Reflect over y-axis
Shifted up 10 units
Shifted right 6 units
d)
Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

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