Q. 78 - Precalculus Enhanced with Graphing Utilities

Question

If the graph of an equation is symmetric with respect to the $y$-axis and 6 is an $x$-intercept of this graph, name another $x$-intercept.

Step-by-Step Solution

Answer

The other $x$-intercept is $-6$.

Step 1: Given information

The $x$-Intercept is $6$, therefore the graph intersects the $x$-axis at $(6,0)$.

Step 2: Determine the other point.

Since the graph is symmetric with respect to the $y$-axis, the following point is also on the graph:

$(-(6), 0)$

Simplify the expression for the first coordinate by changing the sign of the number:

$(-6,0)$

Therefore, the graph contains the point $(-6,0)$.

The graph intersects the $x$-axis at $(6,0)$ because the $y$-coordinate is 0 .

Since the graph intersects the $x$-axis at $(-6,0)$, the $x$-intercept occurs at $-6$.

Step 3: Write the conclusion

The other $x$-intercept is $-6$.