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)

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.