Question

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

Answer 1

C.

EXPLANATION :

From the problem, we have the function :

`y=(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=(x+1)/(x+7)=(-10+1)/(-10+7)=(-9)/(-3) \\ \\ y=3 \end{gathered}`

Since y is positive, the answer is C.