the graph of f(x) = 9(x - 6)/(x² - 7x + 6) has a vertical asymptote at x =

Explanation:

Step1: Factor the denominator

$x^{2}-7x + 6=(x - 1)(x - 6)$ So, $f(x)=\frac{9(x - 6)}{(x - 1)(x - 6)}$

Step2: Find the vertical - asymptotes

Vertical asymptotes occur where the denominator of a rational function is zero and the numerator is non - zero. Set the factored denominator equal to zero: $(x - 1)(x - 6)=0$ Solving $(x - 1)(x - 6)=0$ gives $x = 1$ and $x = 6$. But we can simplify $f(x)$ by canceling out the common factor $(x - 6)$ (for $x\neq6$), and we get $f(x)=\frac{9}{x - 1}$ for $x\neq6$. So the vertical asymptote is at $x = 1$.

Answer:

$1$