Question

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.

Answer 1

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)

with xint at (4,0) and yint at (0,-4)