Answer
Graph of the rational function $r(x)=\frac{3x-12}{x+1}$ is shown below.
The x-intercept occurs at x=4 and the y-intercept occurs at y=-12.
There is a horizontal asymptote at y=3 and a vertical asymptote at x=-1.
The domain of the function is $x\ne-1$ while the range of function is $y\ne-3$
Work Step by Step
The x-intercept occurs at x=4 and the y-intercept occurs at y=-12. This can be observed by making a table of values or by graphing it using transformations.
There is a horizontal asymptote at y=3. This can be determined since the degree of the numerator and denominator are the same so by dividing the leading coefficients (3/1) it is evident the horizontal asymptote occurs at y-3. Also there is a vertical asymptote at x=-1 because -1 will make the denominator 0 and nothing can be divided by 0. Therefore, the domain of the function is $x\ne-1$ while the range of function is $y\ne-3$
