Even Odd Function Graph

4.2 Even and Odd Functions

Notes

Poll

Given the stress of turning in assignments last minute, are you considering to learn a new good habit to help you?

• Yes

• No

• I have a good system

Open Ended

Why are these functions even, what do they have in common?

Multiple Choice

Why are these 3 functions even?

• They are symmetrical about the y axis.

• They all point up

• They have a vertex

Open Ended

What do these odd functions have in common?

Multiple Choice

What makes them odd functions?

• Symmetry about the origin (over both x and y axis)

• Symmetric about x axis

• Rotated 270 degrees

Multiple Choice

Is the function even , odd , or neither?

• Even

• Odd

• Neither

Every point is mirrored across the y-axis

Multiple Choice

Is the function even , odd , or neither?

• Even

• Odd

• Neither

Multiple Choice

Is the function even , odd , or neither?

• Even

• Odd

• Neither

Poll

Which good daily habit do you think you can commit to this six weeks?

• Turn in 1 or 2 assignments per day (for any class).

• Attend all Zoom/Teams Meetings.

• Work for at least an hour a day on school work.

• Log into Canvas and SSS to check grades and assignments.

• Keep a log/ journal / to do list for school work.

Sketch the remaining part of the graph that makes it even or odd

Multiple Choice

Which option shows my EVEN function completed.

Symmetrical about y-axis

Multiple Choice

Which option shows my ODD function completed?

Points reflected over x and y axis (rotated 180 degrees)

Multiple Choice

The algebraic definition of an even function

$$f\left(-x\right)=f\left(x\right)$$  means...

• When you plug in (-x) into the function, you get the original function back.

• The functions are inverses.

• You multiply the function by (-1).

Multiple Choice

The algebraic definition of an odd function

$$f\left(-x\right)=-f\left(x\right)$$  means...

• When you plug in (-x) into the original function, you get the original function times (-1)

• The functions are inverses.

• When you plug in (-x) into the original function you get the original function back.

Multiple Choice

How can we show if it's even or odd algebraically? What's my first step?

• Evaluate at

  $$f\left(-x\right)$$

• Factor the denominator

• Plug in Zero

Multiple Choice

Is the function even or odd?

• Even

• Odd

• Neither

Doesn't match either definition (see * for definition of -f(x) )