STAAR Domain and Range

Algebra I

STAAR REVIEW

Functions - Domain and Range

Functions

There is a relation between the variables x and y.

An ordered pair consists of an x and y coordinate (x, y).

●

x-values: domain, input, independent variable

●

y-values: range, output, dependent variable

A function is a relation in which every input has exactly one
output. ((x-values cannot repeat))

Domain

The domain is all possible x-values.

●Runs from left to right

Range

The range is all possible y-values.

●Runs up and down

How to determine if something is a function:

●

Look at the x-values only!

○

If all x-values are different (x-values do not repeat) then it
IS A FUNCTION

○

The y-values have no bearing in determining functions

A function does not have any repeated x-values.

From Coordinates

​

Multiple Choice

Is this a function?

(Hint: Look only at the x-coordinates)

• Yes, it is a function

• No, it is not a function

Multiple Choice

Is this a function?

(Hint: Look only at the x-coordinates)

• Yes, it is a function

• No, it is not a function

From a table

Multiple Choice

Which relation represents a function?

• Choice One

• Choice Two

Multiple Choice

Which relation represents a function?

• A

• B

Multiple Choice

What is the domain?

• {0, 1, 2, 15}

• (0, 1, 2, 3}

• {3, 7, 11, 15}

• {3, 7, 11, 3}

Multiple Choice

Which table represents a function?

Domain and Range from a Graph

●If a graph is continuous, with an arrow, then the line goes

on forever (∞)

●If a line has a black, shaded in dot, then that value is

included in the domain and range

●If a line has a white, unshaded dot, then that value is NOT
included in the domain and range

Example 3 -

●

What is the domain?

{-7, 1, 5, 7, 8, 10}

●

What is the range?

{1, 0, -7, 5, 2, 8}

From a graph

Discrete Graph

Example 4 -

●

What is the domain?

[0, 45]

●

What is the range?

[10,70]

From a graph

Continuous Graph

Multiple Choice

Is 5 a possible x-value for this function?

• yes

• no

Multiple Choice

Is 0 a possible x-value for this function?

• yes

• no

Multiple Choice

What is the domain of the function? HINT: what letter is being used for x?

• 0<h<80

• 0≤h≤80

• 0≤t≤4.5

• 0<t<4.5

Multiple Choice

Is 2 a possible x-value for this function?

• yes

• no, because a white dot is an excluded value

• no, because a black dot is an excluded value

Multiple Choice

Is -3 a possible x-value for this function?

• no

• yes, because a white dot is an excluded value

• yes, because a black dot is an included value

Multiple Choice

A Water tank is draining and takes a certain amount of time. Which inequality best represents the domain?

• 0 < y < 500

• 500

• 0 < x < 20

• 20

• HINT: What is the smallest x and what is the biggest?

Multiple Choice

What is the range of this graph

• -5 $$\le$$ y $$\le$$ 4

• 4<y<5

• -3<y<2

Multiple Choice

What is the Range?

• y ≥ 6
• y ≤ 6
• -10 ≤ y ≤ 6
• -10 ≤ x ≤ 6

Vertical Line Test

Vertical Line Test says a relationship is a function if a vertical line
drawn through its graph, passes through only one point.

AKA “The Pencil Test”

●

Take a pencil and move it from left to right along the graph. If it
crosses the line at more than one point, then it is NOT a function.

○Remember: X-values cannot repeat!

Multiple Choice

Use the vertical line test

• Function

• Not a Function

Multiple Choice

Is relation shown a function?

• YES
• NO

Multiple Choice

Is the relation a function?

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is y a function of x?

• Function

• Not a function

Practice Problems:

DMAC Test ID: