Graphing Rational Functions

[shell sierra]

Is it that when I have a hole, there isn’t a y-intercept?

[quartz mica]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
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[shell sierra]

Or is it like

Why don’t I have a hole here

[empty marsh]

Given a rational function f(x)/g(x), a hole exists at x=a when f(a) = 0 and g(a) = 0

Ex: x+3/(x^2-9)
Notice how when x=-3, both the top and bottom are 0, so there is a hole at (-3,_)

[shell sierra]

so when f(x) is = to 0

[empty marsh]

Both functions

If only f(x) = 0 then it’s an x-intercept

If only g(x) = 0 then it’s a vertical asymptote

[shell sierra]

ahh okay

so

[shell sierra]

ok but for this one where the degrees of both the numerator and denominator

are the same,

would there ever be a y-int?

[empty marsh]

Degrees of the polynomial only really matter when doing horizontal asympote

[shell sierra]

Noted

ok

[empty marsh]

y-intercept is the y-value when x = 0
Plug in 0 for the equation and see what you get

If you get a number, then that number is y-intercept, else it doesn’t exist

[shell sierra]

so

I thought I plugged in 0 for my hole

which is what I did acc

and it came out as -3/2

however, when I look for a y-intercept in something like mathway, they dont match up

[empty marsh]

When you plug x=0 into the full equation(not simplified) you would get 0/0 which is undefined, therefore there is no y-intercept

[shell sierra]

OH

the original equation

blahj

thank you broski

[cursive cipher]

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