Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

If the graph of an equation is symmetric with respect to the y-axis and -4 is an x-intercept of this graph, then ________ is also an x-intercept.

Step-by-Step Solution

Answer

If the graph of an equation is symmetric with respect to the y-axis and -4 is an x-intercept of this graph, then 4 is also an x-intercept.

Step 1: Given information:

The given statement is

If the graph of an equation is symmetric with respect to the y-axis and -4 is an x-intercept of this graph, then ________ is also an x-intercept.

Step 2:

If a graph is symmetric with respect to y-axis, then the y-values remains unchanged and the x-values changes its sign. 

In this question, the graph is symmetric with respect to y-axis and -4 is an x-intercept $ie, \left(-4,0\right)$, hence same reflected point must be  $\left(4,0\right)$.

Step 3:

On changing the sign  of the point, makes the graph symmetric with respect to y-axis :

If a graph is symmetric with respect to the y-axis and the point (- 4) is on the

graph, then the point 4 is also on the graph.