Exploring Even and Odd Functions

The video tutorial introduces even and odd functions, focusing on their graphical representations. It explains that even functions remain unchanged when reflected over the y-axis, while odd functions remain unchanged when rotated 180 degrees about the origin. The tutorial provides step-by-step instructions on how to determine if a function is even, odd, or neither by analyzing graphs. It includes examples and visual aids to help viewers understand the concepts and apply them to different graphs.

What is the main focus of today's lesson?

• Graphing linear functions

• Graphs of even and odd functions

• Equations of even and odd functions

• Solving quadratic equations

How does an even function behave when reflected over the y-axis?

• It shifts down

• It shifts up

• It rotates 180 degrees

• It remains unchanged

Which of the following is an example of an even function?

• Quadratic function

• Exponential function

• Linear function

• Cubic function

What happens to an odd function when rotated 180 degrees about the origin?

• It remains unchanged

• It reflects over the y-axis

• It shifts to the right

• It shifts to the left

How can you determine if a function is odd using reflections?

• Reflect over the y-axis only

• Reflect over the x-axis only

• Rotate 90 degrees

• Reflect over both the y-axis and x-axis

What is the first step in determining if a function is even?

• Shift the graph up

• Rotate 180 degrees

• Reflect over the y-axis

• Reflect over the x-axis

If a point (2, 2) is reflected over the y-axis, what is the new coordinate?

• (-2, -2)

• (-2, 2)

• (2, 2)

• (2, -2)

What is the new coordinate of (5, 3) when reflected over both the y-axis and x-axis?

• (5, 3)

• (-5, -3)

• (-5, 3)

• (5, -3)

How can you tell if a graph represents an even function?

• It remains unchanged when reflected over the y-axis

• It remains unchanged when rotated 180 degrees

• It shifts up when reflected over the x-axis

• It shifts down when reflected over the y-axis

What type of function is it if a graph does not reflect over the y-axis or rotate 180 degrees?

• Even function

• Odd function

• Both even and odd

• Neither