Free Practice Quiz Question List

04/14 4. Functions and Their Graphs Online Quiz Questions

Use this free practice quiz with 20 questions to review 04/14 4. Functions and Their Graphs, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

Which graph description represents a function of $x$ ?

A
The line $y=2x+1$
B
The circle $x^2+y^2=9$
C
The sideways parabola $x=y^2$
D
A graph containing both $(0,1)$ and $(0,3)$

Choose one

1 point

If $g(x)=f(x-4)$ , how is the graph of $g$ related to the graph of $f$ ?

A
Left 4 units
B
Right 4 units
C
Up 4 units
D
Down 4 units

Choose all

1 point

Select all relations that are functions.

A
$\{(1,2),(2,4),(3,4)\}$
B
$\{(1,2),(2,4),(2,5)\}$
C
$\{(-1,0),(0,0),(1,0)\}$
D
$\{(4,1),(4,2),(5,3)\}$

Choose all

1 point

Select all functions whose real-valued domain is all real numbers.

A
$p(x)=x^4-2x+6$
B
$q(x)=\frac{1}{x-3}$
C
$r(x)=\sqrt{x-2}$
D
$s(x)=|x+8|$

True or false

1 point

True or false: The graph of an inverse relation is the reflection of the original graph across the line $y=x$ .

A
True
B
False

Written response

1 point

Given $f(x)=3x^2-2x+1$ , what is the value of $f(2)$ ?

Written response

1 point

What term names the output variable of a function because its value depends on the input?

Fill in the blank

1 point

For $R=\{(-2,5),(0,1),(3,5),(4,8)\}$ , list the distinct values in increasing order. Domain: . Range: .

Fill in the blank

1 point

Describe the two translations in $g(x)=f(x-5)+2$ : horizontal shift and vertical shift .

Open ended

1 point

Find the inverse function of $f(x)=3x-7$ . Show the algebraic steps used to obtain your answer.

Choose one

1 point

If $f(x)=x^2+4x$ , which expression is equivalent to $f(a+1)$ ?

A
$a^2+4a$
B
$a^2+5a+4$
C
$a^2+6a+5$
D
$a^2+2a+1$

Choose one

1 point

Which relation is not a function?

A
$\{(1,2),(2,3),(3,4)\}$
B
$\{(0,5),(1,5),(2,5)\}$
C
$\{(1,4),(2,6),(2,7)\}$
D
$\{(-1,0),(0,1),(1,0)\}$

True or false

1 point

True or false: If some vertical line intersects a graph at two distinct points, the graph does not represent a function of $x$ .

A
True
B
False

Choose one

1 point

Relative to the parent function $y=x^2$ , what transformation produces $g(x)=(x-4)^2$ ?

A
Left 4 units
B
Right 4 units
C
Up 4 units
D
Down 4 units

Written response

1 point

If $f(x)=x^2+4x$ , what is $f(a+1)$ in fully expanded form?

Choose one

1 point

If $R=\{(1,4),(2,5),(3,7)\}$ , which set is the inverse relation $R^{-1}$ ?

A
$\{(1,4),(2,5),(3,7)\}$
B
$\{(-1,-4),(-2,-5),(-3,-7)\}$
C
$\{(4,5),(5,7),(7,4)\}$
D
$\{(4,1),(5,2),(7,3)\}$

Choose one

1 point

The parent function is $f(x)=|x|$ . What is the vertex of $g(x)=-2|x-3|+1$ ?

A
$(-3,1)$
B
$(3,-1)$
C
$(3,1)$
D
$(-3,-1)$

Choose one

1 point

For a parent function $y=f(x)$ , how does $g(x)=f(2x)$ change horizontal distances?

A
Horizontally stretched by a factor of $2$
B
Horizontally compressed by a factor of $\frac{1}{2}$
C
Vertically stretched by a factor of $2$
D
Vertically compressed by a factor of $\frac{1}{2}$

True or false

1 point

True or false: If the domain of $f(x)=x^2$ is restricted to $[0,\infty)$ , then the inverse relation of $f$ is a function.

A
True
B
False

Written response

1 point

If $f(x)=\sqrt{x}$ and $g(x)=-f(x)$ , across which coordinate axis is the graph of $g$ reflected relative to the graph of $f$ ?