Question

What is the graph of the function f(x) = the quantity of x plus 5, all over x minus 2 ? (1 point) graph with asymptote at x equals negative 3 the portion of the graph to the left extends from y equals one to infinity. The portion to the right extends from negative infinity to asymptote y equals one crossing the x axis at negative 2 graph with asymptote at x equals 2 the portion of the graph to the left extends from y equals one to negative infinity crossing the x axis at negative five. The portion to the right extends from infinity to the asymptote y equals one graph with asymptote at x equals 2 the portion of the graph to the left extends from y equals one to negative infinity crossing the x axis at negative three. The portion to the right extends from infinity to the asymptote y equals one graph with asymptote at x equals negative 2 the portion of the graph to the left extends from y equals one to negative infinity crossing the x axis at negative three. The portion to the right extends from infinity to the asymptote y equals one crossin

Answer 1

C. Graph with asymptote at x =2, the portion of the graph to the left extends from y=1 to negative infinity crossing the x-axis at negative three. The portion to the right extends from infinity to the asymptote y=1.

Explanation:

We have the function
`f(x)=(x+5)/(x-2)`.

First we find the vertical asymptote. They are obtained by the zeros of the denominator.

i.e. x -2 = 0 → x = 2.

Therefore, the function has a vertical asymptote at x =2.

So, the options A) having asymptote at x = -3 and D) having asymptote at x = -2 are not correct.

Now, as the degree of both the polynomials in the numerator and denominator is same.

So, f(x) will not have a slant asymptote but there will exist a horizontal asymptote.

It can be obtained by dividing the leading terms.

i.e.
`y=(x)/(x)` i.e y = 1.

So, the function has a horizontal asymptote at y = 1.

Now, according to the figure below, we can see that the graph on the left extends from y=1 to
`y=-\infty` crossing at x= -2.5 and the graph on the right extends from
`y=\infty` to asymptote y=1.

Hence, the closest answer correct is option C.