Symmetry in Mathematics

Which graph shows line symmetry about the y-axis?

Which graph represents an even function?

Which of the following is an even function?

Which graph shows rotational symmetry?

Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?

F(x) can be odd but cannot be even. What does it indicate?

Which statement best describes how to determine whether f(x) = 9 - 4x^2 is an odd function?

If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?

Line Symmetry

A graph has line symmetry about the y-axis if it can be folded along the y-axis, resulting in both halves matching perfectly.
Graph 'b' demonstrates line symmetry about the y-axis.

Even Functions

An even function is defined by the property that f(x) = f(-x) for all x in its domain.
Graph 'c' represents an even function.
Example of an even function: f(x) = |x|, which is symmetric about the y-axis.

Rotational Symmetry

A graph exhibits rotational symmetry if it looks the same after being rotated about a central point.
Graph 'a' is an example of a graph that shows rotational symmetry.

Increasing Functions

A function f(x) is considered increasing on an interval if for any p < q, f(p) < f(q).
It is possible for a function to be odd (symmetric with respect to the origin) but not even (symmetric with respect to the y-axis), as stated about f(x).

Odd Functions

An odd function meets the condition f(-x) = -f(x) for its domain.
Graphs of odd functions must include symmetrical points in Quadrant IV and the third quadrant due to their symmetry about the origin.

Determining Odd Functions

To verify if a function, such as f(x) = 9 - 4x², is odd, one needs to test whether it satisfies the odd function condition.

This quiz explores various types of symmetry in mathematics, including line symmetry, rotational symmetry, and the properties of even and odd functions. You'll learn how these concepts apply to various graphs and functions, enhancing your understanding of their characteristics.