Question

What is the graph of the function f(x) = the quantity of x plus 2, all over x minus 3

Answer 1

`f(x) = (x + 2)/(x - 3)`

Answer 2

Explanation:

The given function is
`f(x)=(x+2)/(x-3)` and we need to graph it.

In order to graph this function, we'll find below things:

Horizontal asymptote:

Since the degree of both numerator and denominator is same. Hence, the horizontal asymptote is the ratio of leading coefficient of numerator to the leading coefficient of denominator.

Horizontal asymptote is y = 1/1 = 1

Vertical asymptote:

Vertical asymptote occurs where the denominator is zero.

`x-3=0\\x=3`

x-intercepts:

For x-intercept, y = 0

`(x+2)/(x-3)=0\\\\x+2=0\\x=-2`

y-intercepts:

For y-intercept, x= 0

`y=(0+2)/(0-3)=0\\\\y=-(2)/(3)`

Using these, we can draw the graph of the rational expression.