Overview of functions even and odd - Online Tutor - Free Math Videos

The video tutorial explains the concepts of even and odd functions, focusing on their symmetry properties. It describes how even functions are symmetrical about the Y-axis, using parabolas as examples, and how odd functions are symmetrical about the origin, with cubic functions as examples. The tutorial also covers algebraic methods to determine if a function is even or odd by plugging in negative x values and analyzing the output.

What is a key characteristic of an even function's graph?

• It is symmetrical about the X-axis.

• It is symmetrical about the Y-axis.

• It is symmetrical about the origin.

• It has no symmetry.

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

• Exponential function

• Parabola

• Cubic function

• Linear function

How can you test if a function is odd using its graph?

• Check if it is symmetrical about the Y-axis.

• Reflect it about the X-axis and then the Y-axis.

• Check if it is symmetrical about the X-axis.

• Reflect it about the Y-axis and then the X-axis.

What is the result of reflecting an odd function's graph about the Y-axis and then the X-axis?

• The graph becomes symmetrical about the Y-axis.

• The graph becomes symmetrical about the X-axis.

• The graph remains unchanged.

• The graph becomes symmetrical about the origin.

Which of the following statements is true about odd functions?

• They are symmetrical about the Y-axis.

• They have no symmetry.

• They are symmetrical about the X-axis.

• They are symmetrical about the origin.

What happens when you substitute a negative X value into an even function?

• You get a negative output.

• The function becomes undefined.

• You get the same output as the original function.

• You get a positive output.

What is the algebraic test for determining if a function is odd?

• Substitute a positive X and get the same output.

• Substitute a negative X and get the same output.

• Substitute a positive X and get a negative output.

• Substitute a negative X and get a negative output.