Symmetry and Even or Odd Functions

The function shown in the graph is:

• even

• odd

• neither odd nor even

• both odd and even

What type of function is this?

Groups:

(a) ODD FUNCTION

,

(b) EVEN FUNCTION

• Opposite inputs and Same Outputs

• Symmetry at the Origin

• Symmetry at y-axis

• Opposite Inputs and Opposite Outputs

Which one of the following functions is neither even or odd?

• f(x) = x⁴ + x³

• g(x) = x⁴ + x²

• h(x) = x⁵ + x³

• k(x) = x³ + x

Match the following

Groups:

(a) Even Functions

,

(b) Odd Functions

• Rotational Symmetry

• Reflective Symmetry

• Symmetry at the y-axis

• Symmetry at the origin.

Is the following function odd?

• Yes

• No

Is the function even, odd, or neither?

f(x) = x² + 2

• Even

• Odd

• Neither

• Even Function

• Odd Function

• Neither

This has 180˚ rotation symmetry around the origin and the property f(-x)=-f(x).

• Horizontal asymptote

• Vertical asymptote

• Vertical line test

• Odd Function

• Even Function

What type of symmetry does the function have?

• Neither

• Even

• Odd

Which one of the following functions is odd?

• f(x) = 3x⁴ - 4x³

• g(x) = 5x⁴ + 3x²

• h(x) = 6x⁵ - x³

• k(x)=x³+1