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College Algebra: Unit 2 Preview

Total questions: 50

Worksheet time: 3hrs 28mins

Name
Class
Date
1.
What is a function?
a)
For every input, there is exactly one output.
b)
For every output, there is exactly one input.
c)
When there is a polynomial expression
d)
When the degree of the polynomial is even.
2.
What is the domain of a polynomial function?
a)
It depends on the degree of the function being even or odd.
b)
[0,∞)
c)
(-∞,∞)
d)
It depends on the vertex
3.
What is the domain of the following function: f(x)=3x-1
a)
[-1,3]
b)
(-∞,∞)
c)
(-1,∞)
d)
(-∞,-1)
4.
What is the domain of the following graph?
a)
(-∞,∞)
b)
(-∞,4]
c)
(-∞,3]
d)
[-2.5,4]
5.
What is the domain?
a)
The set of all input values
b)
The set of all output values
6.
What is the domain of the following function: ƒ(x)=√(x-10)
a)
(-∞,∞)
b)
[10,∞)
c)
[0,∞)
d)
[0,10]
7.
What is the name of the following function? 
a)
Square Root
b)
Cubic
c)
Linear
d)
Quadratic
8.
What is the RANGE?
a)
{-3, 3]
b)
all real numbers
c)
[-4, 5]
d)
[-4, ∞)
9.

Is the relation shown a function?

a)

No, because the x-value 11 is paired with 5 and 8.

b)

Yes, because each x-value has only one y-value paired with it.

10.

Is this mapping a function and how can you tell?

a)

Yes its a function cause all the numbers have lines

b)

No it's not a function because there a 5 in both ovals

c)

No it's not a function because the x value 5 has 2 outputs.

d)

No it's not a function because the y value 5 has 2 inputs.

11.

The range of a function refers to which variable:

a)

X

b)

Y

c)

Both X and Y

d)

None of the above

12.

Given the domain below listed in interval notation, what is the domain written in inequality notation?

[0, 5)

a)

Domain: 0 < x < 5

b)

Domain: 0 < x < 5

c)

Range: 0 < y < 5

d)

Domain: 0 < x < 5

13.

Given the domain below listed in interval notation, what is the domain written in inequality notation?

(2, 17]

a)

Domain: -2 < x < 17

b)

Domain: -2 < x < 17

c)

Domain: -2 < x < 17

d)

Domain: -2 < x < 17

14.

Given the domain below, written in inequality notation, what is the domain when written in interval notation?

D: -2 < x < 5

a)

(-2, 5)

b)

[-2, 5)

c)

(-2, 5]

d)

[-2, 5]

15.

Given the domain below, written in inequality notation, what is the domain when written in interval notation?

D: 147 < x < 695

a)

(147, 695)

b)

[147, 695)

c)

(147, 695]

d)

[147, 695]

16.

Which of the following graphs has a domain of x > 0 ?

a)
b)
c)
d)
17.

What is the range?

a)

{0, 1, 2, 15}

b)

(0, 1, 2, 3}

c)

{3, 7, 11, 15}

d)

{3, 7, 11, 3}

18.

What is the domain?

a)

{0, 1, 2, 15}

b)

(0, 1, 2, 3}

c)

{3, 7, 11, 15}

d)

{3, 7, 11, 3}

19.

What is the degree of the polynomial y=3y2+y4−7x3+1y=3y^2+y^4-7x^3+1  ?

a)

2

b)

3

c)

4

d)

1

20.

What is the leading coefficient of the polynomial y=5y3+2y6−9x4+x−2y=5y^3+2y^6-9x^4+x-2  ?

a)

-9

b)

2

c)

5

d)

- 2

21.

Is the degree of the graphed polynomial even or odd?

a)

Odd

b)

Even

22.

Is the degree of the graphed polynomial even or odd?

a)

Even

b)

Odd

23.

Using the graph, what can we assume about the equation?

a)

Degree - Even

Leading Coefficient - Positive

b)

Degree - Odd

Leading Coefficient - Positive

c)

Degree - Even

Leading Coefficient - Negative

d)

Degree - Odd

Leading Coefficient - Negative

24.

Using the graph, what can we assume about the equation?

a)

Degree - Even

Leading Coefficient - Positive

b)

Degree - Odd

Leading Coefficient - Positive

c)

Degree - Even

Leading Coefficient - Negative

d)

Degree - Odd

Leading Coefficient - Negative

25.

Using the graph, what can we assume about the equation?

a)

Degree - Even

Leading Coefficient - Positive

b)

Degree - Odd

Leading Coefficient - Positive

c)

Degree - Even

Leading Coefficient - Negative

d)

Degree - Odd

Leading Coefficient - Negative

26.

Using the graph, what can we assume about the equation?

a)

Degree - Even

Leading Coefficient Positive

b)

Degree - Odd

Leading Coefficient Positive

c)

Degree - Even

Leading Coefficient Negative

d)

Degree - Odd

Leading Coefficient Negative

27.
If the blue is f(x)=x2, the red must be
a)
g(x)=(x=3)2
b)
g(x)=x2-3
c)
g(x)=x2+3
d)
g(x)=3x2
28.
If the blue is f(x)=x2, the red must be
a)
g(x)=2x2
b)
g(x)=0.5x2
c)
g(x)=x2+2
d)
g(x)=(x+2)2
29.
 If the blue is f(x)=x3, the red must be
a)
g(x)=x3+1
b)
g(x)=x3-1
c)
g(x)=(x-1)3
d)
g(x)=(x+1)3
30.
Describe the transformation that occurred 
p(x) = f(x + 3)
a)
Horizontal right three units
b)
Dilation three units
c)
Vertical three units
d)
Horizontal Left three units
31.
Which equation describes the transformation of vertical shifting f(x)=x3 four units down?
a)
x3+ 4
b)
x3- 4
c)
(x - 4)3
d)
(x + 4)3
32.
Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units
a)
y = -|x + 2| - 7 
b)
y = |x - 2| - 7 
c)
y = -|x - 2| - 7
d)
y = -|x - 2| + 7
33.
Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units
a)
f(x) = |2x + 1| - 9
b)
f(x) = |2x - 1| - 9
c)
f(x) = 2|x + 1| - 9 
d)
f(x) = 2|x - 1| - 9
34.

Given f(x−3)+5f\left(x-3\right)+5  . What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

35.
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)
36.

Identify the transformation from the graph of  f(x)=sin⁡(x)f\left(x\right)=\sin\left(x\right)  to the graph of g(x)=−sin⁡(x+5)g(x)=-\sin(x+5)  

a)

shifted up five units

reflection in x-axis

b)

shifted down five units

reflection in x-axis

c)

shifted left 5 units

reflection x-axis

d)

shifted right 5 units

reflection x-axis

37.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

38.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

39.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

40.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

41.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

42.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function

43.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function.

44.

The relation in the graph is..

a)

a function but not a one-to-one function.

b)

a one-to-one function.

c)

not a function.

45.
What is the inverse of the points
(1,3)(2,4)(6,8)
a)
(3,1)(4,2)(8,6)
b)
(-3,-1)(-4,-2)(-8,-6)
c)
(1,3)(2,4)(6,8)
d)
(-1,-3)(-2,-4)(-6,-8)
46.
The inverse has been reflected over which line?
a)
y = x
b)
y =1
c)
y = 0
d)
y = x + 1
47.

Which is the inverse of the table?

a)
b)
c)
d)
48.

Are the blue and red graphs inverse functions?

a)

Yes, the functions reflect over y = x

b)

No, they do not reflect over the x - axis.

c)

No way to tell from a graph

49.

Which is f -1(x)?

a)

f -1(x) = 3x + 5

b)

f -1(x) = 3x - 5

c)

f -1(x) = 3x - 15

d)

f -1(x) = 3x + 15

50.
Find the inverse of f(x) = x2 - 5
a)
f-1(x) = √(x) + 5
b)
f-1(x) = ∛(x-5)
c)
f-1(x) =√(x+5)
d)
f-1(x) = x2 - 5

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