Question

what is the vertical asymptote for the rational function $f(x) = \frac{7x+3}{2x-10}$? a $x = 5$ b $x = \frac{7}{2}$ c $x = -\frac{3}{10}$ d $x = -\frac{7}{2}$

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( f(x) = \frac{N(x)}{D(x)} \), vertical asymptotes occur where \( D(x) = 0 \) (and \( N(x)
eq 0 \) at those points).

Step2: Set denominator equal to zero

Given \( f(x) = \frac{7x + 3}{2x - 10} \), set denominator \( 2x - 10 = 0 \).

Step3: Solve for x

Solve \( 2x - 10 = 0 \):
Add 10 to both sides: \( 2x = 10 \).
Divide by 2: \( x = 5 \).
Check numerator at \( x = 5 \): \( 7(5) + 3 = 38
eq 0 \), so vertical asymptote is \( x = 5 \).

Answer:

A. \( x = 5 \)