Comparing Linear Functions

Functions Unit Review LESSON

Functions, Linear Functions, Writing Equations for Functions, and Comparing Functions

Unit 4 Standards

• MGSE8.F.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

• MGSE8.F.2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• MGSE8.F.3. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

• MGSE8.F.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

What is a function?

• A relation or set of ordered pairs in which each input (domain value or x value) has only ONE output (range value or y value).

Multiple Choice

What is the definition of function?

• Has inputs and outputs

• Each input has only ONE output

• Inputs have different outputs every time

• x-values and y-values

Functions in Graphs

Use the vertical line test, to determine if a relation is a function. If a vertical intersects the graphed image at more than one point, it is not a function.

Multiple Choice

Is this graph a function or not a function?

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function 

Functions in Tables

Check the input or x values. If there are NO repeating values in the inputs, IT IS A FUNCTION.

Multiple Choice

Is the relation a function?

• yes, it is a function
• no, it is not a function
• not enough information to determine

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Functions in Ordered Pairs

The same as a table, check the x values. If there are no repeating Xs, IT IS A FUNCTION. Each input can only have one output.

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Functions in a Mapping Diagram

Check the inputs. Since each input can only have one output, each input can only be mapped to one output. (If one input has more than one line mapped to an output, it is not a function.)

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

Identifying Linear Functions in:

Equations

Graphs

Tables

Identifying Linear Functions in a Graph

If the graph is a straight line, it is a LINEAR function.

Multiple Select

Select the graphs that shows a linear function.

Multiple Choice

Why is this function linear?

• This is a linear function because it is going up
• This is a linear function because it is a straight line.
• This is a linear function because the line is curved.
• This is a linear function because it keeps going.

Multiple Choice

Why is this function nonlinear?

• This is a nonlinear function because it is on the side.

• This is a nonlinear function because it is a straight line.

• This is a nonlinear function because the line is curved.

• This is a nonlinear function because it is open ended

Linear Functions in an Equation

If the equation is in the form of or can be put in the form of y = mx + b, IT IS A LINEAR FUNCTION.

x is your input

y is your output

m is your slope

b is your y intercept

Nonlinear Examples in Equations

*No exponent other than 1
*The variable can not be in the denominator

 $y=\frac{5}{x}$  

Multiple Choice

Is the following equation linear or nonlinear? 

• Linear 
• Nonlinear 

Multiple Choice

Is the following equation linear or nonlinear? 

• Linear 
• Nonlinear 

Multiple Choice

LINEAR or NONLINEAR?

y = 7x³ + 5

• linear

• nonlinear

Linear Functions in Tables

The slope or rate of change ratios must be equivalent for every x and y in the table.

 $\frac{\Delta\ y}{\Delta\ x}$  

Multiple Choice

Why is this function linear?

• This is a linear function because it does not have a constant rate of change

• This is a linear function because it creates a curved line.

• This is a linear function because it have a constant rate of change.

• This is a linear function because it's y-intercept is (0,2)

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the table linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Which answer choice is true?

• The table represents a linear function because there is a pattern for the x-coordinates and y-coordinates.
• The table represents a linear function because the ratio of the change in the y value and the change in the x value is constant.
• The table represents a nonlinear function because the ratio of the change in the y value and the change in the x value is not constant.
• The table does not represent a function because there is more than one output for at least one input.

Writing Equations of Linear Functions

From a graph, table, and word description

Writing an Equation from a table

y = mx + b

m = slope

b = y-intercept (find in the table or plug in values for x and y to solve for b)

Multiple Choice

What is the equation of the linear function?

• y = -3x + 10
• y = -3x + 16
• y = 3x + 10
• y = 3x + 16

Multiple Choice

Which equation matches the table?

• y = 3x + 9

• y = x + 9

• y = x + 3

• y = 12x - 3

Writing Equations from a Graph

y = mx + b
1. Find slope (m)  $\frac{rise}{run}$  

2. Find y-intercept (b) where the graphed line crosses the y axis 

Multiple Choice

Which equation matches the graph? (Click me to see the image)

• y = 2x
• y = 1/4 x + 2
• y = 1x + 4
• y = -2x

Multiple Choice

Write the equation of the line.

• y= -1x-3
• y= -3x-1
• y=-1/3x-1
• y= -3x-3

Writing an Equation from a Verbal Description

*m is the slope/rate of change (look for key words: per, each, every...) happens repeatedly

*b is the y-intercept/initial value and occurs once in the problem (look for key words: starts, begins...)

Multiple Choice

Amelia has $100 in her savings account and plans on solving $20 per week. Write an equation to represent this situation.

• y = 100x

• y = 20x

• y = 20x + 100

• y = 100x + 20

Multiple Choice

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation to represent this situation.

• y = 2x + 15

• x = 15y + 2

• y = 15x+ 2

Comparing Linear Functions

1. Find the slope/rate of change for each

2. Find the y-intercept/initial value for each

3. Compare

Multiple Choice

Compare the rates of change. Which statement is true about functions A and B?

• They have the same rate of change

• A has a greater rate of change than B

• A and B both have negative rates of change

• A has a negative ROC and B has a positive ROC

Multiple Choice

Who has the greater rate of change?

• Braden has the greater rate of change with 60/3
• Omar has the greater rate of change with 100
• Braden has the greatest rate of change with 60
• They both have the same rate of change

Multiple Choice

Who has the greater rate of change?

• Hunter has the greater rate of change.
• Casey has the greater rate of change 
• They have the same rate of change