Understanding Even, Odd, and Neither Functions

The video tutorial explains how to determine if a graph represents an even, odd, or neither function. It describes the characteristics of even functions, which have symmetry across the y-axis, and odd functions, which have rotational symmetry about the origin. The tutorial uses three graph examples to illustrate these concepts: the first graph is even, the second is odd, and the third is neither. The video provides step-by-step analysis and verification using specific points on the graphs.

What characteristic does an even function's graph exhibit?

• Symmetry across the y-axis

• No symmetry

• Rotational symmetry about the origin

• Symmetry across the x-axis

Which of the following is true for an odd function?

• f(x) = f(x)

• f(x) = -f(-x)

• f(x) = f(-x)

• f(x) = 0

What type of symmetry does an odd function's graph have?

• Symmetry across the x-axis

• Symmetry across the y-axis

• No symmetry

• Rotational symmetry about the origin

In the first graph, what is the y-value when x is 4?

• 1

• 4

• 2

• 3

For the first graph, what is f(-4) if f(4) = 3?

• 1

• 2

• 3

• 4

What happens when you fold the second graph across the y-axis?

• The graph disappears

• The halves match perfectly

• The halves do not match

• The graph rotates

What is the result of rotating the second graph 180 degrees?

• The graph disappears

• The graph looks the same

• The graph looks different

• The graph flips upside down

In the second graph, what is the y-value when x is -1?

• 2

• 0

• 1

• -2

What is required for a graph to have rotational symmetry about the origin?

• No rotation

• Less than one complete rotation

• Two complete rotations

• One complete rotation

What is the conclusion for the third graph?

• It is an even function

• It is both even and odd

• It is an odd function

• It is neither even nor odd