Is Y x symmetric about the origin?

Algebra Examples Since the equation is not identical to the original equation, it is not symmetric to the y-axis. Check if the graph is symmetric to the origin by plugging in −x for x and −y for y . Since the equation is identical to the original equation, it is symmetric to the origin.

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.

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

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 is symmetric about the origin?

A graph is said to be symmetric about the origin 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 origin.

How do you find the x-axis symmetry?

To check for symmetry with respect to the x-axis, just replace y with -y and see if you still get the same equation. If you do get the same equation, then the graph is symmetric with respect to the x-axis.

How do you find the symmetry of the x-axis?

A graph is said to be symmetric about the x -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 x -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) .

What is X Y symmetry?

How do you know if a function has origin symmetry?

Another way to visualize origin symmetry is to imagine a reflection about the x-axis, followed by a reflection across the y-axis. If this leaves the graph of the function unchanged, the graph is symmetric with respect to the origin.

Which is symmetric Y or X on the x axis?

Use the same idea as for the Y-Axis, but try replacing y with −y. Example: is y = x 3 symmetric about the x-axis? Try to replace y with −y: Try multiplying both sides by − 1: It is different. Try swapping y and x (i.e. replace both y with x and x with y).

When do X and Y have origin symmetry?

They are the same. Origin Symmetry is when every part has a matching part: but in the opposite direction. Check to see if the equation is the same when we replace both x with −x and y with −y. Example: does y = 1/x have Origin Symmetry?

Is the Y Y axis the same as the original equation?

So, some terms have the same sign as the original equation and other don’t so there isn’t symmetry about the y y -axis. Finally, check for symmetry about the origin. Again, this is not the same as the original equation and isn’t exactly the opposite sign from the original equation and so isn’t symmetric about the origin.

Which is an example of symmetry in a graph?

For example, the graph of a circle centered at the origin exhibits all three symmetries. We’ve some fairly simply tests for each of the different types of symmetry. A graph will have symmetry about the x x -axis if we get an equivalent equation when all the y y ’s are replaced with – y y.