What equation is symmetric with respect to the origin?

What equation is symmetric with respect to the origin?

The graph of an equation is symmetric with respect to the origin if replacing x with –x and y with –y yields an equivalent equation. A function is called even if it is symmetry with respect to the y-axis. A function is called odd if it is symmetric with respect to the origin.

How do you show that a function is symmetric to the origin?

when a function is symmetric about y-axis then, f(x)=f(−x) f ( x ) = f ( − x ) . when a function is symmetric about origin then, f(x,y)=f(−x,−y) f ( x , y ) = f ( − x , − y ) .

What is the symmetric formula?

The symmetric form of the equation of a line is an equation that presents the two variables x and y in relationship to the x-intercept a and the y-intercept b of this line represented in a Cartesian plane. The symmetric form is presented like this: xa+yb=1, where a and b are non-zero.

How do you find the equation of a line that is symmetrical?

You can use the formula x = -b / 2a to find the line of symmetry. Vertex form is y = (x – h)^2 + k. where h = x and k = y. Identify which number is -h in the equation, and then write the opposite of -h for your line of 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. These are two types of symmetry we call even and odd functions.

How do you find a slope?

Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: Slope =riserun Slope = rise run .

How do you determine whether a graph is symmetric with respect to 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) .

How do you write slope?

The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It’s usually easy to graph a line using y=mx+b. Other forms of linear equations are the standard form and the point-slope form.

How do you know if a graph is symmetric with origin?

To check for symmetry with respect to the origin, just replace x with -x and 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 origin. Example #3:

What does symmetric with respect to the origin mean?

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.

Does y = 1/x have origin symmetry?

Start with: y = 1/x. Replace x with − x and y with − y: ( −y) = 1/ ( −x) Multiply both sides by − 1: y = 1/x. And we have the original equation. So y = 1/x has Origin Symmetry. Amazing! y = 1/x has origin symmetry as well as diagonal symmetry!

Which equation is symmetric with respect to the Y-axis?

Since replacing x with -x gives the same equation, the equation y = 5x 2 + 4 is symmetric with respect to the y-axis. Test for symmetry with respect to the origin. The graph of a relation is symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x, -y) is also on the graph. Example #3: