## Can a function be symmetric about the y-axis and the origin?

On the other hand, a function can be symmetric about a vertical line or about a point. In particular, a function that is symmetric about the y-axis is also an “even” function, and a function that is symmetric about the origin is also an “odd” function.

### What functions are symmetric across the y-axis?

A function symmetrical with respect to the y-axis is called an even function. A function that is symmetrical with respect to the origin is called an odd function. f(x). Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.

#### How do you find the origin of symmetry of a function?

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. So there is no symmetry about the origin, and the answer is Symmetrical about the x-axis.

How do you find the symmetry of a rational function?

Test to see if the graph has symmetry by plugging in (-x) in the function. Options: If the signs all stay the same or all change, f(-x) = f(x), then you have even or y-axis symmetry. If either the numerator or the denominator changes signs completely, f(-x)= -f(x) then you have odd, or origin symmetry.

What does symmetric with respect to the y-axis mean?

Functions can be symmetrical about the y-axis, which means that if we reflect their graph about the y-axis we will get the same graph. There are other functions that we can reflect about both the x- and y-axis and get the same graph.

## What is origin symmetry?

Symmetric about the Origin. Symmetric across the Origin. Symmetric with Respect to the Origin. Describes a graph that looks the same upside down or right side up. Formally, a graph is symmetric with respect to the origin if it is unchanged when reflected across both the x-axis and y-axis.

### What is the y-axis?

A coordinate grid has two perpendicular lines, or axes (pronounced AX-eez), labeled just like number lines. The horizontal axis is usually called the x-axis. The vertical axis is usually called the y-axis. The point where the x- and y-axis intersect is called the origin.

#### How do you write the axis of symmetry?

The symmetry cuts any geometric shape into two equal halves. The axis of symmetry formula is given as, for a quadratic equation with standard form as y = ax2 + bx + c, is: x = -b/2a. If the parabola is in vertex form y = a(x-h)2 + k, then the formula is x = h.

Which graph is symmetric about y-axis?

A graph is said to be symmetric about the y -axis if whenever (a,b) is on the graph then so is (−a,b) . Here is a sketch of a graph that is symmetric about the y -axis. A graph is said to be symmetric about the origin if whenever (a,b) is on the graph then so is (−a,−b) .