Characteristics of Parent Functions

1
Characteristics of Parent Functions

• Six Types of Parent Graphs
• Linear ymxb
• Quadratic yx2
• Cubic yx3
• Rational y1/x
• Absolute Value yx
• Square Root yvx

2
Characteristics we will look for

• Domain What xs does the graph use.
• Range What ys does the graph use.
• Intervals of Increasing What xs make the ys
  increase.
• Intervals of Decreasing What cs make the ys
  decrease.
• Zeroes Also called x-intercepts or solutions.
  Where does the graph cross the x-axis.

3
Characteristics we will look for

• Y-intercepts Where does the graph cross the
  y-axis.
• Right Hand Behavior As the xs get really large
  where do the ys want to head.
• Left Hand Behavior As the xs gofurther and
  further negative where do the ys want to head.

4
Linear ymxb

• b is your y-intercept
• m is you slope
• Graph like you did in 8th grade

5
Linear Characteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

6
Linear Characteristics

• Right Hand Behavior
• Left Hand Behavior
• These will all depend upon which linear equation
  you are given.

7
Quadratic Equation yx2

• Shape is a parabola, a u-shaped graph.

8
Quadratic Characteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

9
Quadratic Characteristics

• Right Hand Behavior
• Left Hand Behavior

10
Cubic Equation yx3

• The shape is a stretched out N or S.

11
Cubic Characteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

12
Cubic Characteristics

• Right Hand Behavior
• Left Hand Behavior

13
Rational Equation y1/x

• This graph has asymptotes, you cant divide by
  zero or get a y-value of zero.

14
Rational Equation Characteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

15
Rational Equation Characteristics

• Right Hand Behavior
• Left Hand Behavior

16
Absolute Value Equation yx

• V-shaped graph.

17
Absolute Value Charcteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

18
Absolute Value Characteristics

• Right Hand Behavior
• Left Hand Behavior

19
Square Root Function yvx

• Starts at x0 and goes up very slowly.

20
Square Root Characteristics

• Domain
• Range
• Interval of Increasing
• Interval of Decreasing
• Zero
• Y-intercept

21
Square Root Characteristics

• Right Hand Behavior
• Left Hand Behavior