Consider the function f(x) = the quantity x squared minus x minus 12 all over the quantity x plus 3. describe the graph of this function. include all discontinuities, intercepts, and the basic shape of the graph.

First, substitute the value of x into the function, that would be that is now f(x) = x-4, cancelling -3. We have to do this to get the point of discontinuity

Your remaining function now is f(x) = x-4, which is a line. Find the value of the x-intercept by making y to 0 and vice versa when finding the value of the y-intercept.

After cancelling the (x+3) from both the numerator and the denominator, your point discontinuity happens when the factor is equal to zero. This happens after you substitute x= -3 into the new function that is y=x-4, so you will get -7. So the point discontinuity lies at the f(-3)=-7 or (-3, -7).

Find the value of the x- intercept and y-intercept, you equate it with zero, that would be

0= x-4 x=4 (4, 0).

 y= 0 - 4 y= -4 (0, -4).

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