How do you complete a graph to make it look symmetric with respect to x-axis?

Answer 1

leave the x values as they are and multiply all your y values by -1.

Answer 2

Flip your graph over the x-axis and superimpose the result on the original.

If your graph is defined by the functon f(x), then taking -f(x) flips the graph over the x-axis. When you superimpose the graph of -f(x) on the graph of f(x) you no longer have a function, however, since there are two y-values for every x-value.

The poster above only describes how to find the mirror image of your graph about the x-axis, he doesn't explain how to make your graph symmetric. You need to superimpose the mirror image on the original.

Taking the absolute value of the right hand side of the function that defines the graph, as the poster below suggested, generates symmetry about the y-axis, not the x-axis. And this method does not "complete" the graph, it changes it on the negative domain.

However, if you want to define the solution by using absolute values, then you can do the following: If you original graph is defined by f(x), then the graph defined by g(x) = |f(x)| + |f(-x)| will give the desired result.

Be careful, however, because this can get tricky. For example if your original function is f(x) = x+1, then the relation that defines a completed, x-symmetric version of your graph is g(x) = |x+1| + |-x+1|. Note that g(x) is now the independent variable, and f(x) has been evaluated at x and -x to give you the right hand side.

I hope that helps.

Answer 3

Not every equation will be symmetric with respect to the x-axis or the y-axis. In drawing a graph, the goal is to show key information about how that particular equation behaves. In the case of a line, you would want to show the x-intercept and the y-intercept. For a parabola or higher order quadratic functions, you would want to show the turning points. Equations that are symmetric with respect to the x-axis will not be functions, because for the same value of x, you will have both a positive y and negative y that are the same distance, in different directions, from the x-axis.

Answer 4

What kind of symmetry? Mirror, rotoplane.... There are many kinds of symmetry. If you mean a mirror symmetry about the y axis, I would take each coordinate in the first quadrant and graph the same point with the negative of the y coordinate. So (1,2) would have a corasponding point at (1,-2) and so on. Of course if this graph is valid assumes the graph of whatever equation you are graphing would be symmetrical about the x axis

Answer 5

with respect? never heard that one before... but you can at least flip it over the y right?

Answer 6

use absolute value
Y= abs value of x