Question

identify the vertical asymptote of the function.
$f(x)=-\frac{7}{x - 2}+7$

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( f(x)=\frac{g(x)}{h(x)} \), vertical asymptotes occur where \( h(x) = 0 \) (and \( g(x)
eq0 \) at those points). The given function \( f(x)=-\frac{7}{x - 2}+7 \) has a rational part \( -\frac{7}{x - 2} \). The denominator of the rational part is \( x - 2 \).

Step2: Solve denominator for zero

Set the denominator equal to zero: \( x - 2=0 \). Solving for \( x \), we add 2 to both sides: \( x=2 \). We check that the numerator of the rational part (which is -7) is not zero at \( x = 2 \), so \( x = 2 \) is a vertical asymptote.

Answer:

The vertical asymptote of the function \( f(x)=-\frac{7}{x - 2}+7 \) is \( x = 2 \).