Free Printable Analyzing Functions

1.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

2.

All of the x values or inputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

3.

All of the y values or outputs are called what?

a)

Domain

b)

Range

c)

Relation

d)

Function

4.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

5.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

6.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

7.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

8.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

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

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

9.

What is the range?

a)

x≥0

b)

y≥0

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

10.

a)

{1, 2, 3, 4, 5}

b)

{-1, 1, 2, 3}

c)

{1, 2, 3, 5}

d)

[1, 5]

11.

What is the Range of the situation?

a)

$0\le x\ \le9$

b)

$0<x<9$

c)

$0<x<28$

d)

$0\le y\le28$

12.

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. The equation: C=2h+15. If Frank wants to rent the boat from to 3 to 6 hours, what is the domain and range?

a)

Domain: 3 < x < 6

Range: 21 < y< 27

b)

Domain: 3 < x < 6

Range: 21 < y < 27

c)

Domain: {3, 4, 5, 6}

Range: { 21, 23, 25 , 27}

d)

Domain: { 21, 23, 25 , 27}

Range: {3, 4, 5, 6}

13.

What is the domain of the graph shown?

a)

{-2, -1, 0, 1, 2, 3, 4}

b)

{2, 3, 4}

c)

2 ≤ y ≤ 4

d)

-2 ≤ x ≤ 4

14.

Express the following in Interval Notation
-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

15.

Express the following in Interval Notation
-9 < x ≤ -4

a)

[-9, -4]

b)

(-9,-4]

c)

[-9, -4]

d)

(-9,-4)

16.

What is the domain of the function?

a)

(3, ∞)

b)

[-3, ∞)

c)

(-∞, 4]

d)

(-∞, 4)

17.

What is the domain?

a)

(-3 , 3)

b)

[-4, 5]

c)

(-4, 5)

d)

(-3, 3]

18.

What is the range?

a)

(-3, 3)

b)

[-4, 5)

c)

[-4 , 5]

d)

(-3 , 3]

19.

Which function family does this graph belong to?

a)

Exponential

b)

Linear

c)

Cubic

d)

Absolute Value

20.

Which function family does this graph belong to?

a)

Absolute Value

b)

Cubic

c)

Quadratic

d)

Exponential

21.

Name the parent function.

a)

constant

b)

quadratic

c)

linear

d)

exponential

22.

What type of function is this?
$y=3\left|x+1\right|+4$

a)

Linear Function

b)

Quadratic Function

c)

Absolute Value Function

d)

Exponential Function

23.

What is the range of the graph?

a)

$\left[2,\ \infty\right)$

b)

$\left[1,\ \infty\right)$

c)

$\left(-\infty,\ \infty\right)$

d)

None of these

24.

What function family is this graph from?

a)

Reciprocal/Rational

b)

Exponential/Logarithmic

c)

Polynomial

d)

Absolute Value

25.

What function family do I belong to?

a)

Linear

b)

Quadratic

c)

Exponential

d)

Linear Absolute Value

26.

Which parent function matches the graph?

a)

f(x) = √(x)

b)

f(x) = ∛(x)

c)

f(x) = |x|

d)

f(x) = a⋅b^x

27.

If f(x) = -4x - 5 and
g(x) = 3 - x,
what is g(-4) + f(1)?

a)

7

b)

-2

c)

-9

d)

-10

28.

Use the graph to evaluate $f\left(3\right)$

a)

1.5

b)

5

c)

3

d)

8

29.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

30.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

31.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

32.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

33.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

34.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

35.

a)

Translation

b)

Reflection

c)

Rotation

d)

Dilation

36.

Describe the transformation that is applied to the parent function.
f(x) = IxI -5

a)

Shifts left 5

b)

Shifts right 5

c)

Shifts up 5

d)

Shifts down 5

37.

Tell how the graph transformed.
y = (x - 3)²

a)

Translated right 3

b)

Translated left 3

c)

Translated up 3

d)

Translated down 9

38.

What shifts have occurred?

a)

left 1, up 5

b)

left 1, down 5

c)

right 1, down 5

d)

right 1, up 5

39.

Which equation below is a quadratic function translated left 4 units?

a)

y = x² + 4

b)

y = (x + 4)²

c)

y = (x - 4)²

d)

y = 4x²

40.

Describe the transformation from the parent absolute value function:

$y=\left|x\right|-5$

a)

Shift up 5 units

b)

Shift down 5 units

c)

Shift right 5 units

d)

Shift left 5 units

41.

Which function has a range of $\left[0,\ \infty\right)$ ?

a)

Linear

b)

Quadratic

c)

Square Root

d)

Cubic

e)

Cube Root

42.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

43.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

44.

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

a)

Horizontal shift left 6, vertical shift up 2

b)

Horizontal shift left 6, vertical shift down 2

c)

Horizontal shift right 6, vertical shift down 2

d)

Horizontal shift right 6, vertical shift up 2

45.

A student graphed $f\left(x\right)=x$ and $g\left(x\right)=f\left(x\right)+3$ on the same coordinate grid. Which statement describes how the graphs of $f$ and $g$ are related?

a)

The graph of $f$ is shifted 3 units up to create the graph of $g$ .

b)

The graph of $f$ is steeper than the graph of $g$ .

c)

The graph of $f$ is shifted 3 units down to create the graph of $g$ .

d)

The graph of $f$ is less steep than the graph of $g$ .

46.

The graph of $f\left(x\right)=x^2$ was translated $4.5$ units to the left to create the graph of function $g$ . Which function represents $g$ ?

a)

$g\left(x\right)=\left(x-4.5\right)^2$

b)

$g\left(x\right)=\left(x+4.5\right)^2$

c)

$g\left(x\right)=x^2-4.5$

d)

$g\left(x\right)=x^2+4.5$

47.

The graph of $f\left(x\right)=x^2$ was transformed to create the graph of $g\left(x\right)=f\left(x\right)-9$ . Which statement about the graphs is true?

a)

The graph of $g$ is a reflection of the graph of $f$ across the x-axis.

b)

The vertex of the graph of $g$ is $9$ units to the right of the vertex of the graph of $f$ .

c)

The graph of $g$ is a reflection of the graph of $f$ across the y-axis.

d)

The vertex of the graph of $g$ is $9$ units below the vertex of the graph of $f$ .

48.

How does the graph of f(x) = -(x - 5)²compare to the graph of the parent quadratic function?

a)

5 units left

b)

5 units right

c)

5 units left and reflection in the x-axis

d)

5 units right and reflection in the x-axis

49.

Match the description with the transformation.

g(x)= -f(x) - 4

a)

Reflected over x axis and up 4

b)

Reflected over x axis and down 4

c)

Reflected over y axis and right 4

d)

Reflected over y axis and left 4

50.

Given f(x) = f(-x), how did we transform from the parent function?

a)

Reflection over the y-axis

b)

Reflection over the x-axis

c)

Moved down

d)

got wider

Analyzing Functions

Total questions: 50

Worksheet time: 2hrs 44mins

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