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.

f(x)=((x-4)(x+3))/(x+3)

simpify

f(x)=x-4

see we eliminated x+3?

That is a hole

find the value of that hole

x+3=0

x=-3

input into simplified function

f(-3)=-3-4

f(-3)=-7

the hole (discontinuity) is at (-3,-7)

f(x)=x-4

where does it cross x axis?

0=x-4

4=x

xint is x=4 or (4,0)

yint is where x=0

f(0)=0-4=-4

yint is (0,-4)

basically

it is a line, f(x)=x-4 with a hole at (-3,7)

30

step-by-step explanation:

times by times

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right