Function Families

Function Families

Constant Function

• f(x)=a

• horizontal line

• no curves, bends, or points

Multiple Select

Select all the Constant functions

Linear Function

• f(x)= mx+b or f(x)=ax+b

• Line

• No curves, points, or bends

• Can be horizontal and diagonal, but CANNOT be vertical

• Root Word LINEar Function (line)

Multiple Select

Select all Linear Functions

Quadratic Function

•  $f\left(x\right)=ax^2+bx+c$  

• Parabola (horseshoe shape or U shape)

• Both sides go the same direction, either both up or both down

Multiple Select

Select all the Quadratic Functions

Cubic Functions

•  $f\left(x\right)=x^3$  

• S shaped

• One side goes up, one side goes down

Multiple Select

Select all the Cubic Functions

Absolute Value Function

•  $f\left(x\right)=a\left|x-h\right|+k$  

• V Shaped

• Both sides will go the same direction

• Easy way to remember absolute Value is V-shaped

Multiple Select

Select all the Absolute Value Functions

Linear Piecewise Functions

• Includes a combination of lines and line segments

• No specific Shape

• Can be symmetrical, but is not a requirement

• Can touch, but can be disconnected

Multiple Select

Select all the Linear Piecewise Functions

Continuous vs Discrete

• Continuous graphs have no breaks in them (you could draw them without picking up your pencil)

• Discrete graphs are disconnected (you would have to pick up your pencil to draw them)

Multiple Select

Select all the discrete graphs

Multiple Select

Select all the continuous graphs

Multiple Choice

What function family do I belong to?

• Linear
• Quadratic
• Exponential
• Linear Absolute Value

Multiple Select

What kind of function is represented by the RED line?

• constant

• linear

• quadratic

• exponential

Multiple Choice

Identify the function family.

• Linear

• Exponential

• Quadratic

• Constant

Multiple Choice

Identify the function family.

• Linear

• Exponential

• Quadratic

• Constant

Multiple Choice

What family of function is this?

• Cubic

• Cube Root

• Absolute Value

• Logarithmic

Multiple Choice

What family of function is this?

• Square root

• Reciprocal

• Exponential

• Quadratic

Multiple Choice

What family of function is this?

• Linear

• Quadratic

• Exponential

• Reciprocal

Multiple Select

Which equation(s) is written in function notation?

•  $f\left(x\right)=4x+2$  

•  $y\ =\ 2x^2+5x-6$  
  

•  $h\left(x\right)=4^x-2$ 

•  $5y-2x=15$  
  

Multiple Choice

Which Function family do I belong to?

• Linear Piecewise

• Absolute Value

• Quadratic

• Cubic