Question

At which values of x does the graph of the function F(x) have a vertical asymptote? Check all that apply

Answer 1

Step 1:

Write the rational expression:

`\begin{gathered} f(x)\text{ = }(x+4)/(x^2+5x-24) \\ \end{gathered}`

Step 2:

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value).

Step 3

`\begin{gathered} x^2+5x-24=0 \\ \\ x^2+8x\text{ - 3x - 24 = 0} \\ \\ x(x\text{ + 8\rparen-3\lparen x + 8\rparen = 0} \\ \\ (x\text{ - 3\rparen\lparen x + 8\rparen = 0} \\ \\ x\text{ - 3 = 0, x + 8 = 0} \\ x\text{ = 3, x = -8} \end{gathered}`

Step 4:

\ertical} Asymptote is =-8,\ =3,