## How do you find the symmetry of a function on a graph?

Algebraically check for symmetry with respect to the x-axis, y axis, and the origin. For a function to be symmetrical about the origin, you must replace y with (-y) and x with (-x) and the resulting function must be equal to the original function.

## Which functions have graphs that are symmetrical?

Even functions A function is said to be an even function if its graph is symmetric with respect to the y-axis.

**What are the types of symmetry in graphs?**

There are three types of graphical symmetry you may be responsible for: x-axis, y-axis, and origin. Knowing the properties of symmetry can help you when sketching complex graphs.

### What is symmetry of a function?

A symmetry of a function is a transformation that leaves the graph unchanged. Consider the functions f(x) = x2 and g(x) = |x| whose graphs are drawn below. Both graphs allow us to view the y-axis as a mirror. A reflection across the y-axis leaves the function unchanged. This reflection is an example of a symmetry.

### How do you find the axis of symmetry on a graph?

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

**What types of functions have symmetry?**

An even function has reflection symmetry about the y-axis. An odd function has rotational symmetry about the origin.

## What is symmetry in a graph?

A graph is symmetric with respect to a line if reflecting the graph over that line leaves the graph unchanged. This line is called an axis of symmetry of the graph. x-axis symmetry. A graph is symmetric with respect to the x-axis if whenever a point is on the graph the point is also on the graph.

## What does symmetric graph mean in math?

A symmetric graph is a graph that is both edge- and vertex-transitive (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive or a 1-arc-transitive graphs are sometimes also known as symmetric graphs (Godsil and Royle 2001, p. 59).

**What is the axis of symmetry example?**

The axis of symmetry is an imaginary straight line that divides the shape into two identical parts or that makes the shape symmetrical. For example, a square has 4 and a rectangle has 2 axes of symmetry.

### What is symmetry function?

### Is the graph of a function symmetric to the Y axis?

In general, for any even function f (x) f (x), the the graph of f (x) f (x) is symmetric about the y y -axis; for any odd function

**What is symmetry in Algebra?**

Because of this correspondence between the symmetry of the graph and the evenness or oddness of the function, “symmetry” in algebra is usually going to apply to the y -axis and to the origin. In what follows, list any symmetries, if any, for the displayed graph, and state whether the graph shows a function.

## What is the symmetry of graph E?

Graph E: This graph (of a square-root function) shows no symmetry whatsoever, but it is a function. Graph F: This graph (of a cubic function) is symmetric about the point (–4, –1), but not around any lines.

## What are some examples of symmetric graphs?

Examples. In general, for any even function f(x), the the graph of f(x) is symmetric about the y -axis; for any odd function g(x), the graph of g(x) is symmetric about the origin. See Sine and Cosine graphs for more properties of the sine and cosine graphs.