Question

graph the following rational function.
$f(x) = \frac{-x + 1}{x^2 - 64}$
step 1 of 3 : plot the vertical asymptotes, if any, on the graph.
answer
once the number of asymptotes is selected, that number of lines are available to plot. select a location on the grid to plot a line. lines can be moved by dragging or using the arrow keys.
number of vertical asymptotes:
\bigcirc none \bigcirc one \bigcirc two

Explanation:

Step1: Find denominator roots

For vertical asymptotes, set denominator \(x^2 - 64 = 0\).
Solve \(x^2 = 64\), so \(x = \pm 8\) (since \(x^2 - 64=(x - 8)(x + 8)\)).

Step2: Check numerator at roots

Numerator at \(x = 8\): \(-8 + 1=-7
eq0\).
Numerator at \(x = -8\): \(-(-8)+1 = 9
eq0\).
So two vertical asymptotes (\(x = 8\) and \(x = -8\)).

Answer:

Number of Vertical Asymptotes: Two
Then plot vertical lines \(x = -8\) and \(x = 8\) on the graph.