TOOLKIT FUNCTIONSPRE-CALCULUS

ECHS SPRING 2016

Parent Functions and their “Children”

A Parent function is the most “BASIC” form of the function.

All other functions of this type are transformations from the parent.

They look like their Parent function, but have been changed in either

- Size (Dilation)

- Position on Coordinate Plane (Translation Up/Down and/or Right/Left)

- Orientation (Reflection)

(We will leave Rotations for Calculus!)

Toolkit Functions that you should know!

Linear Function

Square Root Function

Quadratic Function

Cubic Function

Rational Function

Logarithmic Function

Exponential Function

Absolute Value Function

What should you know about each function?What is the Graph of the function?

What is the Domain and Range?

On what intervals is it Increasing or Decreasing?

Does it have a Maximum or Minimum (local extrema)?

Where are the X-Intercept(s)?

Where is the Y-Intercept?

What are the End Behaviors?

Does it have any Asymptotes?

Is it Symmetric?

Is it a Continuous function?

EXAMPLE - • Name: Quartic Function

• Quartic Functions can be used to find the intersection of Conic Sections (Ellipses/Hyperbolas/Circles/Parabolas)

• Domain has no restrictions therefore (-, ); Range is limited from the origin upwards therefore [0, )

• The function decreases from (- , 0] and increases from [0, )

• The function has a minimum value at the origin (0, 0) and increases without bound therefore it has no maximum.

• Both the x – and y – intercepts are at (0, 0). It can have up to 4 x-intercepts.

• The left hand behavior:

• The right hand behavior:

• There are no asymptotes.

• This function is symmetric across the y-axis.

• The function is continuous.

Look up the listed Toolkit Functions

Sketch a parent graph for each and write the Domain and Range.