Identifying Types of Functions

Identifying Types of Functions

By Angela Weisheyer

MA.912.F.1.1

Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.

• Clarification Within the Algebra 1 course, functions represented as tables are limited to linear, quadratic and exponential.

Multiple Choice

Linear, Quadratic, and Exponentials are types of ___?

• Functions

• math problems

• shapes

• Triangles

Identifying functions from a Graph

The graph of a Linear Function is one straight line.

Increasing lines have a positive slope.

Decreasing lines have negative slope.
Horizontal lines have a 0 slope
Vertical Line are not a function and have an undefine slope

​Quadratics make a u shape that is called a parabola.

Concave Up parabola have a minimum. Both end behaviors increase.

Concave Down parabola have a maximum. Both end behaviors decrease.

​Exponential Functions makes a curve shape.

Increasing exponentials are called growth.
Decreasing exponentials are called decay

Exponential have an asymptote where the graph approaches but does not cross.

Multiple Select

Select all correct answers.

Types of Linear Functions are...

• Increasing

• Decreasing

• Horizontal

• Vertical

Multiple Choice

Which linear has a negative slope

• Increasing

• Decreasing

• Horizontal

• Vertical

Multiple Choice

Which linear has a 0 slope

• Increasing

• Decreasing

• Horizontal

• Vertical

Identifying functions from a Graph

The graph of a Linear Function is one straight line.

Increasing lines have a positive slope.

Decreasing lines have negative slope.
Horizontal lines have a 0 slope
Vertical Line are not a function and have an undefine slope

​Quadratics make a u shape that is called a parabola.

Concave Up parabola have a minimum. Both end behaviors increase.

Concave Down parabola have a maximum. Both end behaviors decrease.

​Exponential Functions makes a curve shape.

Increasing exponentials are called growth.
Decreasing exponentials are called decay

Exponential have an asymptote where the graph approaches but does not cross.

Multiple Select

What is true about this graph?

Select All

• Concave Up

• Concave Down

• Has a Maximum

• Has a Minimum

Multiple Select

What is true about this graph?

Select All

• Concave Up

• Concave Down

• Has a Maximum

• Has a Minimum

Identifying functions from a Graph

The graph of a Linear Function is one straight line.

Increasing lines have a positive slope.

Decreasing lines have negative slope.
Horizontal lines have a 0 slope
Vertical Line are not a function and have an undefine slope

​Quadratics make a u shape that is called a parabola.

Concave Up parabola have a minimum. Both end behaviors increase.

Concave Down parabola have a maximum. Both end behaviors decrease.

​Exponential Functions makes a curve shape.

Increasing exponentials are called growth.
Decreasing exponentials are called decay
Exponential have an asymptote where the graph approaches but does not cross.

Multiple Select

Select all

This Exponential graph is ...

• Decreasing

• Decaying

• Increasing

• Growth

Multiple Choice

Exponential graphs always have a/an ...

• x-intercept

• two x-intercepts

• asymptote

• Maximum

Identifying functions from a Graph

The graph of a Linear Function is one straight line.

Increasing lines have a positive slope.

Decreasing lines have negative slope.
Horizontal lines have a 0 slope
Vertical Line are not a function and have an undefine slope

​Quadratics make a u shape that is called a parabola.

Concave Up parabola have a minimum. Both end behavior increase.

Concave Down parabola have a maximum. Both end behaviors decrease.

​Exponential Functions makes a curve shape.

Increasing exponentials are called growth.
Decreasing exponentials are called decay

Exponential have an asymptote wear the graph approaches but does not cross.

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Multiple Choice

This graph is

• Linear

• Quadratic

• Exponential

• Neither

Identifying functions from an Equation

Linear equations have a degree of 1.

The exponent of x and y is an invisible 1

Quadratic equations have a degree of two.

The highest exponent of x is 2.

​Exponential equations have an x as the exponent.

Multiple Select

Select all Linear Equations

• y = 3x + 2
• $$y=x^2+7$$

• $$y=\ 8^x-1$$

• y = 4
• 2x + 3y = 7

Multiple Select

Select all Exponential Equations

• y = (3x + 2)(x + 5)

• $$y=x^2+7$$

• $$y=\ 8^x-1$$

• y = 4
• $$y=7\left(0.25\right)^{3x}$$

Multiple Select

Select all Quadratic Equations

• y = (3x + 2)(x + 5)

• $$y=x^2+7$$

• $$y=\ 8^x-1$$

• y = 4
• $$y=7\left(0.25\right)^{3x}$$

Identifying functions from a Table

Linear tables have a constant rate of change

Every y minus the previous y will result in the same answer

Exponential tables have a constant factor

Every y divided by the previous y will result in the same answer

​Quadratic Tables have a constant 2nd difference.

The y values are symmetrical and will repeat.

Multiple Choice

Which function type has y values that can repeat?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

Which function type has an multiplication pattern?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

Which function type has an addition pattern?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

Which type of function is given by the table?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

What type of function is given in the table?

• linear
• Exponential

• Quadratic

• None of the above

Multiple Choice

This table represents what kind of function?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

Is the table linear, exponential or neither?

• Linear

• Exponential

• Quadratic

• None of the Above

Multiple Choice

Is this table linear, quadratic, exponential, or none of the above?

• linear
• exponential

• quadratic

• None of the Above

Multiple Choice

Which type of function is given by the table?

• Linear

• Exponential

• Quadratic

• None of the Above