Question

list any vertical asymptotes for the function given below.
f(x)=\frac{3(x - 17)}{x - 7}
oa. ( x = 17 )
ob. ( x = 7 )
oc. ( y = 0 )
od. ( x = 0 )

Explanation:

Step1: Recall the definition of vertical asymptote

A vertical asymptote occurs at \(x = a\) if the denominator of a rational function \(f(x)=\frac{N(x)}{D(x)}\) is zero at \(x = a\) and the numerator \(N(a)
eq0\).

Step2: Set the denominator equal to zero

For the function \(f(x)=\frac{3(x - 17)}{x - 7}\), set \(D(x)=x - 7=0\). Solving \(x-7 = 0\) gives \(x = 7\).

Step3: Check the numerator at \(x = 7\)

Substitute \(x = 7\) into the numerator \(N(x)=3(x - 17)\). Then \(N(7)=3(7 - 17)=3\times(- 10)=-30
eq0\).

Answer:

B. \(x = 7\)