Linear Functions

Pre-algebra Topics

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Welcome toyour Toolbox

Vocabulary

1. Function:a mathematical relation for which each ____________ of the domain corresponds to exactly one element of the range

1. Linear Function: a function that has a ____________ rate of change

Toolbox Tutor:Vocabulary Review (1:04)

Graphs of Linear Functions

You have learned that a ____________ is a relation where each x-value is paired with exactly one y-value.

In other words, the domain values, or x-values, do not repeat.

A linear function is a special type of function that has a constant rate of change, or slope.

Toolbox Tutor:Practice Problem 1 (2:27)

__________________ __________________

__________________ __________________

Equations of Linear Functions

The equations of linear functions have an independent and a dependent variable, each with an exponent of 1.

Remember that when there is an exponent of 1, you do not need to write the exponent.

The equations of nonlinear functions have variables with exponents that are not 1, or the variable itself is an exponent.

Important Note: Horizontal lines and their equations are considered functions.This is because each input (x) value is paired with a single _________ (y) value.

The graphs and equations of VERTICAL lines are not functions. This is because there is a single _________ (x) value paired with multiple output (y) values.

Toolbox Tutor:Practice Problem 2 (4:11)

Equation	Linear or Nonlinear
y = -4x + 7
Why?:

Equation	Linear or Nonlinear
x =34
Why?:

Equation	Linear or Nonlinear
x =y2+3
Why?:

Equation	Linear or Nonlinear
y =79
Why?:

Tables of Linear Equations

Not only can linear functions be represented by a graph or an equation, but they can also be shown in a table of input-output values.

A table represents a linear function when there is a constant rate of change.

Rate of change, or slope, is found by finding the change in the y-values, divided by the change in the x-values.

If the inputs change by the same amount and the outputs change by the same amount, then the function has a constant rate of change and is linear.

Toolbox Tutor:Practice Problem 3 (2:21)

x	y

This function is ___________________ because

there ______________ a constant rate of change

Toolbox Tutor:Practice Problem 4 (2:10)

x
y

This function is ___________________ because

there ______________ a constant rate of change

Toolbox Tutor:Practice Problem 5 (2:43)

x	y

This function is ___________________ because

there ______________ a constant rate of change