Identifying Linear Functions

Identifying Linear Functions

I can identify linear functions and linear equations.

This graph represents a function because  each domain value(x-value) is paired with exactly one range value (y-value). 

A function whose graph forms a straight line is called a linear function.

Multiple Choice

Which graph is linear?

• A

• B

• C

• D

Multiple Choice

Identify the graph.

• Non-Linear Functions
• Linear Function
• Not A Function
• A Sad Face

Multiple Choice

Is the function linear or nonlinear?

• Linear Function
• Nonlinear Function

Multiple Choice

Is the function linear or nonlinear?

• Linear Function
• Nonlinear Function

You can sometimes identify a linear function by looking at a table or a list of ordered pairs.

In a linear function, a constant change in x corresponds to a constant change in y.

The points from the chart create a line, therefore it shows a linear function.

In this table, a constant change of +1 in x does not correspond to a constant change in y.

These points do not satisfy a linear function.

The points from this table do not lie on a line, therefore it is not a linear function.

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Identify the table that represents a linear function.

• Table 1
• Table 2
• Table 3
• Table 4

Multiple Choice

• Yes
• No

Multiple Choice

• Yes
• No

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Standard Form of a Linear Equation

• Ax+By=C where A, B & C are real numbers and A & B are not both 0.

• 3x+2y=10 (Linear because it matches standard form of a line.)

• y-2=3x (Linear because you can rearrange and get 3x-y=-2)

• -y=5x (Linear because you can rearrange and get 5x+y=0)

• y=10 (Linear because it matches standard form of a line; 0x+y=10)

What won't match standard form of a line?

• 3xy+x=1 (Not linear, because you can't have two variables multiplied by each other.) 

•  $x^2+y=1$  (Not linear, because x can only have an exponent of 1.)

•  $x+\frac{6}{y\ }=12$  (Not linear, because x and y cannot be in the denominator.)

• y=|x+4| (Not linear, because it x cannot be inside an absolute value.)

Multiple Choice

• Linear Function
• Nonlinear Function

Multiple Choice

• Linear Function
• Nonlinear Function

Multiple Choice

What is the formula for standard form?

• y=mx+b
• y-y₁=m(x-x₁)
• Ax+By=C
• rise÷run

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the table linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this equation a linear function: 3y = 12

• Yes
• Not enough information
• No

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function

Multiple Choice

• Yes
• No

Multiple Choice

Is this a function or not a function?

• Function
• Not a Function

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

What type of function is y=2x+4?

• Linear

• Nonlinear

• Absolute Value

• Exponential

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Is this function linear or non linear?

• Linear
• Non Linear

Multiple Choice

Linear functions cannot have __________.

• An x nor a y
• x + y
• x - y
• xy

Multiple Choice

Which of the following is NOT a linear function?

• y = 3x
• y = x²
• y = 5x - 9
• y = 3(x + 4)

Functions Review

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

What is the vertical line test?

• A graph is not a function if you can draw a vertical line and it crosses the graph in more than 1 location

• A Graph is a function if it can be altered to make a linear equation.

• A graph is a function if you can create a vertical line that adheres to the equation y=mx+b

• Stay within the vertical lines

Multiple Choice

Is this is a function or not a function?

• Function
• Not a Function