Question

Sketch the graph of the rational function. y = x+1 / x + 7Choose the correct graph below.

Answer 1

ANSWER :

C.

EXPLANATION :

From the problem, we have the function :

$y=\frac{x+1}{x+7}$

The vertical asymptote is at x when the denominator is equal to 0.

That's

x + 7 = 0

x = -7

From the options, only A and C have vertical asymptote at x = -7

Next is to substitute x = -10

As we can see from A and C,

For A, when x = -10, y is negative

For C, when x = -10, y is positive

Substitute x = -10 :

$\begin{gathered} y=\frac{x+1}{x+7}=\frac{-10+1}{-10+7}=\frac{-9}{-3} \\ \\ y=3 \end{gathered}$

Since y is positive, the answer is C.