Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

If for every point (x, y) on the graph of an equation the point (-x, y) is also on the graph, then the graph is symmetric with respect to the ___________.

Step-by-Step Solution

Answer

If for every point (x, y) on the graph of an equation the point (-x, y) is also on the graph, then the graph is symmetric with respect to the  y-axis .

Step 1: Given information:

The given statement is

If for every point (x, y) on the graph of an equation the point (-x, y) is also on the graph, then the graph is symmetric with respect to the ___________.

Step 2:

A graph is said to be symmetric, if it remains unchanged when reflected over a line.

Example: $f\left(x\right)=x^2$

The above graph is symmetric with respect to y-axis. Graph remains unchanged when folded along y-axis.

Also, In the graph, the points $\left(1,1\right)$ has its reflection $\left(-1,1\right)$ and $\left(2,4\right)$has its reflection at $\left(-2,4\right)$. We can observe that the y-values remains unchanged and x-values changes its sign.