Free Printable Function Families Review

1.

Which type of function is represented by the graph?

a)

Exponential

b)

Quadratic

c)

Square Root

d)

Absolute Value

2.

Which type of function is shown in the graph?

a)

Quadratic

b)

Square Root

c)

Natural Logarithm

d)

Rational

3.

Which is the parent function of the graph?

a)

f(x) = log x

b)

f(x) = x³

c)

f(x) = 1 ∕ x

d)

f(x) = ∛x

4.

Which type of function is the graph?

a)

Absolute Value

b)

Rational

c)

Exponential

d)

Logarithmic

5.

Which of the graphs could represent the graph of y = − (x − 3)² ?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

6.

Which graph represents

y = |x + 3| − 4 ?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

7.

What is the correct transformed equation for the graph?

a)

y = $\sqrt{x}-4$

b)

y = $\sqrt{x}+4$

c)

y = $\sqrt{x-4}$

d)

y = $\sqrt{x+4}$

e)

y = $4\sqrt{x}$

8.

What is the correct transformed equation for the graph?

a)

y = ln(x - 4)

b)

y = ln(x) - 4

c)

y = ln(x + 4)

d)

y = ln(x) + 4

9.

Which most likely represents the equation of this graph?

a)

y = |x + 2| + 3

b)

y = |x - 3| + 2

c)

y = |x + 3| + 2

d)

y = |x - 2| + 3

10.

What is the range of the function graphed?

a)

(-∞, ∞)

b)

(-∞, 2] and [2, ∞)

c)

[2, ∞)

d)

(2, -∞)

11.

What is the domain of the function graphed?

a)

(-∞, ∞)

b)

[-5, ∞)

c)

[-5, -4]

d)

[-4, ∞)

12.

What is the range of the function graphed?

a)

(-∞, -3]

b)

(-∞, ∞)

c)

[-4, -1]

d)

[-3, ∞)

13.

Name the y-intercept(s) of the function in the graph.

a)

(-1, 0) and (4, 0)

b)

(-2, 0)

c)

(0, -2)

d)

(0, 4) and (0, -1)

14.

Name the x-intercept(s) in the graph.

a)

(-4, 0) and (2, 0)

b)

(-2, 0)

c)

(0, -2)

d)

(0, -4) and (0, 2)

15.

Which function increases throughout
the interval (-2, 2)?

a)

b)

c)

d)

16.

Name the interval(s) where the function is increasing? Click all that apply.

a)

$\left(-\infty,\ -1\right)$

b)

$\left(-1,\ 1\right)$

c)

$\left(-2,\ 2\right)$

d)

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

17.

Which statement is true about the end behavior of the function

y = -3x²?

a)

As x approaches negative infinity, y approaches 0.

b)

As x approaches positive infinity, y approaches negative infinity.

c)

As x approaches positive infinity, y approaches 0.

d)

As x approaches negative infinity, y approaches positive infinity.

18.

Which of the following describes an end behavior of the function graphed? Select all that apply.

a)

As x → -∞, y → -∞

b)

As x → -∞, y → +∞

c)

As x → +∞, y → -∞

d)

As x → +∞, y → +∞

19.

What is the domain of the function:

f\left(x\right)\ =\ x^2-3

a)

$\left(0,\infty\right)$

b)

$\left(-\infty,0\right)$

c)

$\left(3,\infty\right)$

d)

$\left(-\infty,3\right)$

e)

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

20.

What is the range of this function:

f\left(x\right)=\sqrt{x+2}-1

a)

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

b)

$\left(-1,\ \infty\right)$

c)

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

d)

$\left(-\infty,-1\right]$

e)

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

21.

Which function family does this graph belong to?

a)

Exponential

b)

Linear

c)

Cubic

d)

Absolute Value

22.

Which function family does this graph belong to?

a)

Absolute Value

b)

Cubic

c)

Quadratic

d)

Exponential

23.

What is the domain?

a)

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

b)

$\left[0,\ \infty\right)$

c)

$\left(-\infty,\ 0\right]$

d)

$\left[-\infty,\ \infty\right]$

24.

Identify the transformation(s).
$y=3\left|x+1\right|+4$

a)

down 4

b)

right 1

c)

left 1

d)

vertical stretch

e)

up 4

25.

What is the range?

a)

\left(0,\ \infty\right)

b)

$\left[0,\ \infty\right)$

c)

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

d)

None of the answer choices

26.

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

27.

Describe the end behavior of the graph.

a)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

b)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow\infty$

c)

None of these

d)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow-\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

28.

Describe the end behavior of the graph.

a)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

b)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow\infty$

c)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow0$

d)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow0$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

29.

Describe the end behavior of the graph.

a)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$

and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

b)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow\infty$

c)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow0$

d)

$x\rightarrow\infty\ as\ f\left(x\right)\rightarrow-\infty$ and $x\rightarrow-\infty\ as\ f\left(x\right)\rightarrow-\infty$

30.

What are the increasing interval(s)?

a)

( - ∞, 0)

b)

(-7, ∞)

c)

(0, 2)

d)

( -∞, -3)

e)

(2, ∞ )

31.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

32.

Which of the following is the graph of $y=\left(x-2\right)^3-4$

a)

b)

c)

d)

33.

What are the zeros of the given graph? Select all that apply.

a)

$-3$

b)

$0$

c)

$1.5$

d)

$3$

34.

Which of the following represents the graph below?

a)

b)

c)

d)

35.

What is the range for the following function?

a)

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

b)

$\left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$

c)

$\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$

d)

$\left(-\infty,\ -4\right)\cup\left(-4,\ \infty\right)$

e)

$\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)$

36.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

37.

What of the domain of the function?

a)

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

b)

$\left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$

c)

$\left(-\infty,\ -3\right)\cup\left(-3,\ \infty\right)$

d)

$\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$

e)

$\left(-\infty,\ 3\right)\cup\left(3,\ \infty\right)$

38.

What is the range of y = sin x ?

a)

$\left(-1,\ 1\right)$

b)

$\left[-1,\ 1\right]$

c)

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

d)

$\left[-1,\ 0\right)$

39.

What is the range of y=3sin(x+1)-2

a)

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

b)

$\left[-3,\ 3\right]$

c)

$\left[-5,\ 1\right]$

d)

$\left(-3,\ 3\right)$

e)

$\left(-5,\ 1\right)$

40.

A function is vertically shrunk, shifted down, shifted left and reflected over the x axis. Which of the following could be that function? (check all that apply)

a)

$f\left(x\right)=\frac{5}{4}\left(x+1\right)^2-6$

b)

$f\left(x\right)=-\frac{5}{6}\sqrt{x+2}-3$

c)

$f\left(x\right)=-6\left|x+3\right|+4$

d)

$f\left(x\right)=-\frac{1}{2x+6}-3$

e)

$f\left(x\right)=-\frac{3}{4}e^{\left(x-2\right)}-7$

Function Families Review

Total questions: 40

Worksheet time: 40mins

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