Question

What is the graph of the function f(x) = the quantity of x squared plus 3 x minus 4, all over x plus 4 ?

Answer 1

\[\frac{ x^2 + 3x - 4 }{ x + 4 }\]

Answer 2

hint: try factoring the numerator

Answer 3

heh, or we could factor out the top and simplify.

\[\frac{ (x+4)(x-1) }{ (x+4) }\]

Answer 4

What would my Y-int be?

Answer 5

-4?

Answer 6

Look at @Photon336 's last post. Notice that the numerator is factored. A pair of terms will cancel.

Answer 7

what is left behind?

Answer 8

Oh, so x-1

Answer 9

yes, so that complicated rational expression is equivalent to x-1

The only subtle difference is that there's a hole on the line y = x-1. Where is the hole?

Answer 10

yeah heh, always see if you can factor the numerator or denominator in these problems, to see if you can simplify the question any further.

Answer 11

@marinadanyel if you need to graph functions desmos is a good site to do that.

Answer 12

Where does the Y-int come in?

Answer 13

I'm not sure where the hole is

Answer 14

At x = -4 , the zeros of the denominator

Answer 15

Think of y = x - 1 as y = 1*x + (-1)

The equation `y = 1*x + (-1)` is in the form `y = mx+b`

Answer 16

(3, -7)

Answer 17

that's where the hole is?

Answer 18

close but no

Answer 19

notice how -4 makes the denominator of the original expression equal to 0

x+4 = -4+4 = 0

so the hole will be when x = -4

plug x = -4 into y = x-1 to find the y coordinate of this hole

Answer 20

(-4, -5)

Answer 21

yes

Answer 22

Okay, I see, I didn't understand the substitution at first.

Answer 23

Thanks!

Answer 24

no problem