Question

7 of 10this quiz: 10 point(s) possiblethis question: 1 point(s) possiblefind the x- and y-intercepts of the graph of the given equation.$y=\frac{x+2}{2x-7}$find the x-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choicea. the x-intercept(s) is/are $x=$(simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using radicals as needed. use a comma to sep as needed.)b. there are no x-interceptsfind the y-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choicea. the y-intercept(s) is/are $y=$(simplify your answer. use integers or fractions for any numbers in the expression. type an exact answer, using radicals as needed. use a comma to sep as needed.)b. there are no y-intercepts

Explanation:

Step1: Find x-intercept (set $y=0$)

Set $y=0$, so $\frac{x+2}{2x-7}=0$. A rational function equals 0 when its numerator is 0 (denominator ≠0).
Solve $x+2=0$
$x=-2$
Check denominator: $2(-2)-7=-4-7=-11≠0$, so valid.

Step2: Find y-intercept (set $x=0$)

Set $x=0$, substitute into $y=\frac{x+2}{2x-7}$
$y=\frac{0+2}{2(0)-7}=\frac{2}{-7}=-\frac{2}{7}$

Answer:

For x-intercept:

A. The x-intercept(s) is/are $x=-2$

For y-intercept:

A. The y-intercept(s) is/are $y=-\frac{2}{7}$