Question

question 5 of 24 step 1 of 3 consider the following rational function. \\( f(x) = \frac{-2x - 5}{x - 4} \\) step 1 of 3: find equations for the vertical asymptotes, if any, for the function. answer how to enter your answer (opens in new window) 2 points separate multiple equations with a comma. selecting a button will replace the entered answer value. the value of the button is used instead of the value in the associated box. none keypad keyboard shortcuts

Explanation:

Step1: Recall vertical asymptote rule

For a rational function \( f(x)=\frac{N(x)}{D(x)} \), vertical asymptotes occur where \( D(x) = 0 \) (and \( N(x)
eq0 \) at those points).
Here, \( D(x)=x - 4 \), set \( x - 4=0 \).

Step2: Solve for x

Solve \( x - 4 = 0 \), we get \( x = 4 \).
Check \( N(x)=-2x - 5 \) at \( x = 4 \): \( N(4)=-2(4)-5=-8 - 5=-13
eq0 \). So \( x = 4 \) is a vertical asymptote.

Answer:

\( x = 4 \)