Question

Someone please help me! I have been asking these two questions all day and no ones seems to know how to do them. HELP!

Answer 1

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 2

Ah, it's a simple graphing rational expressions problem.

Answer 3

I will give medal or whatever you want just please can you tell me what the answer is and how you got it?

Answer 4

Begin by factoring the numerator.

Answer 5

Can you do that?

Answer 6

You have x^2 -x -12 in the numerator. Its factors are (x-4)(x+3), but that is all divided by (x+3), so a factor cancels. When this occurs, you know your function has a hole when x = -3.

Answer 7

ok but how do I answer what it is asking?

Answer 8

Plug that x value into the function, that is now f(x) = x-4, where x cannot be -3, to find the y value and the point of the discontinuity.

Answer 9

This is part of the sol'n, lol, the point discontinuity or the "hole" in the function.

Answer 10

oh. so where are my intercepts?

Answer 11

Your remaining function now is f(x) = x-4, which is a line.
Your x-intercept can be found by making "y" equal to 0.
Similarly, the y-intercept can be found by making the "x" value 0.

Answer 12

This line, remember, has a hole at the point (-3, -7).

Answer 13

So thode would be the intercepts?

Answer 14

and wait would my point of discontinuity be -7?

Answer 15

@KinzaN are you still here?

Answer 16

Yes, sorry. Well since you cancelled the factor (x+3) from both the numerator and the denominator, your hole or point discontinuity occurs when that factor is equal to 0, which is when x = -3.

Plugging that value of x=-3 into your new function, y=x-4, results in an answer of -7.

So your hole lies at the point f(-3)=-7 or (-3, -7).

Answer 17

wait so my point of discontinuity is -7 then what are my intercepts?

Answer 18

ugh this is confusing

Answer 19

You find values on your x-axis--or x-intercepts--when your y-value is 0.

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

And,
y= 0 - 4
y= -4
(0, -4).

Answer 20

ooooohhhhh ok. and I would describe the shape of the graph as a straight line right?

Answer 21

A line with a slope of one and y-intercept of -4 with a hole at (-3, -7), I guess would be an awesome answer. :)

Answer 22

Lol ok. Can you help me with one more? I am about to post it.

Answer 23

Haha, oookay. :) I'm avoiding my own homework by doing homework for others online, I've got time.

Answer 24

Lol ok THANK YOU!