Question

question 5 of 10, step 1 of 3
graph the following rational function.
$f(x) = \frac{-x - 4}{x^2 - 36}$
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:
none one two

Explanation:

Step1: Find denominator roots

To find vertical asymptotes, set the denominator equal to zero: \(x^2 - 36 = 0\).

Step2: Solve the equation

Factor the equation: \((x - 6)(x + 6)=0\). Solving gives \(x = 6\) and \(x=-6\). These are two distinct roots, so there are two vertical asymptotes.

Answer:

Two (and then plot the lines \(x = 6\) and \(x=-6\) on the graph)