Question

question 5 of 10, step 2 of 3
graph the following rational function.
$f(x) = \frac{-x - 4}{x^2 - 36}$
step 2 of 3 : plot the horizontal 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 horizontal asymptotes:
none one two
(graph with x and y axes from -10 to 10)

Explanation:

Step1: Analyze degrees of numerator and denominator

The rational function is \( f(x)=\frac{-x - 4}{x^{2}-36} \). The degree of the numerator (highest power of \( x \)) is \( 1 \) (from \( -x \)), and the degree of the denominator is \( 2 \) (from \( x^{2} \)).

Step2: Determine horizontal asymptote rule

For a rational function \( \frac{N(x)}{D(x)} \), if the degree of \( N(x) \) (\( n \)) is less than the degree of \( D(x) \) (\( m \)), the horizontal asymptote is \( y = 0 \) (the x - axis). Here, \( n = 1 \), \( m = 2 \), so \( n

Answer:

One (and the horizontal asymptote is \( y = 0 \), which is the x - axis, so we would plot the x - axis as the horizontal asymptote)