Lesson 4: Relations and Functions

Lesson 4: Relations and Functions

How do we relate two different values using algebra?

​What is a Relation?

​A "relation" is a pairing of input values with output values.

​The set of input values is called the domain and the set of output values is called the range.

​Find the domain and range of this relation

​Practice!

​Functions

For every function, there is only one y-value per x-value (or, one output per input). So,

if you can plug in an

input and get two

different answers,

then the relation is

not a function.​

​Functions

We can identify functions one of two ways: checking if any x-value has two or more

​y-values, or using the

​vertical line test on

​relation graphs.

​

​In the vertical line test,

​if you draw a vertical

​line through the graph

​and hit two points on the graph, then it is not a function.

​Is the above relation a function?

​Practice!

Multiple Choice

Identify the domain of the relation.

• -9, -5, 1, 7

• 1, 4, 5, 8

• -9, -5, 1, 1, 7

• 4, 8

​Relations in Two Variables

​An equation in two variables can relate two values like in the equation: y = 2x + 3. The input variable, x, is the independent variable and the output value, y, is the dependent variable (since its value depends on the value of the input).

​Graphing an Equation

​To graph an equation in two variables, we select values for x, plug them in to the equation, and then solve for y. This gives us a coordinate pair (x, y) that we can plot on a Cartesian plane.

​

​The relation to the right is a function and is linear.

​

​NOTE: When working with functions, we sometimes use function notation which is written f(x) = mx + b, and f(x) stands in place of y.

NOTE:​

Functions which contain variables with exponents are not linear.

Examples: y = 4x³ - 8, and y = 2x² + 4x - 16 are not linear since one x-value in each has an exponent attached to it.​

Multiple Choice

Is the following relation linear?

$$y=2x-8$$  

• Yes

• No

Fill in the Blanks

Solve for x = 3 in the following equation:

$y=2x-8$