Need up to 30 seconds to load.

in this lesson we're going to talk about

how to find the X and the y-intercepts

of a rational function

let's begin by finding

the y-intercept first

in order to find the y-intercept

we need to set x equal to zero and we

need to solve for y

let's go ahead and do that

so we're going to have 8

minus 2 times 0 over 5.

minus 3 times 0.

now zero times anything is zero so we

simply get eight over five as our answer

so that's the y-intercept now we could

write the answer as an ordered pair

we can write it as zero comma eight over

five

so that's all you need to do in order to

find the y-intercept

now let's get the x-intercept

in order to find the x-intercept

y equal to zero and then solve for x

so we're going to have zero is equal to

eight minus two x over five minus 3x

now what I'm going to do is I'm going to

rewrite zero as a fraction 0 is

equivalent to 0 over 1.

now we can cross multiply so I have 1

times 8 minus 2x which is just 8 minus

2X

and that equals zero times five minus 3x

now zero times anything is simply zero

next we can add 2x to both sides so we

get 8 is equal to 2X

and then to isolate X we could divide

both sides by two

so X is eight over two

which is 4.

so the x-intercept is going to be 4

comma zero as an ordered pair

so that's how we could find the X and

the y-intercepts of a rational function

so remember in order to find the

x-intercept

y equal to zero in order to find

the y-intercept set x equal to zero and

solve for y

for the x-intercept after you set y

equal to zero then you can solve for x

now let's try another problem

let's say we have y is equal to 8

divided by x minus 3.

go ahead and find the X and the

y-intercepts for this particular

rational function

so let's start with the y-intercept

so let's set x equal to zero

this is going to be eight over zero

minus three

zero minus three is negative 3. so we

simply get negative eight over three

so we can write our answer as zero comma

negative eight over three

so that's the y-intercept

for this particular problem

now let's focus on

the x-intercept

so this time we're going to set y equal

to zero and we're going to solve for x

so zero is equal to eight over x minus

three

let's put this over one and cross

multiply

one times eight is eight zero times x

minus three is zero eight does not equal

zero

so when you get an unequal expression

like this it means that there is no

x-intercept there's none

so that's it for this problem

now let's move on to the next one

let's say we have y

is equal to x squared minus 7x Plus 12.

and this is going to be divided by

3x squared minus 48.

so go ahead and find the X and Y

intercepts for that particular rational

function

now before we start this problem

we should attempt to factor every

possible expression that we can

so let's go ahead and do that it'll make

the math a lot easier

so how can we Factor this trinomial

where the leading coefficient is one

what we need to do is find two numbers

that multiply to 12 but add to the

middle coefficient negative seven

four times three is twelve

and the same is true from negative 4

Negative 3. they multiply to positive

12. but they add to a negative seven so

to factor the numerator it's going to be

x minus 4.

times x minus 3.

now for the denominator the first thing

we need to do is take out the GCF which

is 3.

3x squared divided by 3 is x squared

negative 48 divided by 3 is negative 16.

now we have a difference of two squares

so to factor it it's going to be X plus

4 and x minus 4.

you take the square root of x squared

that'll give you X and then the square

root of 16 will give you 4.

1 will be positive the other will be

negative

so notice that we have a common factor

that we could cancel out which is x

minus 4.

so we're left with x minus 3 divided by

three

X Plus 4.

so now let's go ahead and find

the y-intercept

so we're going to set x equal to zero

and we're going to solve for y

so this is 0 minus 3 over 3

times 0 Plus 4.

zero plus four is four

we could cancel a three

and so we're left with negative one over

four

so we can write the y-intercept as zero

comma negative one over four

now let's focus on the x-intercept

so this time we're going to set y

equal to zero and we're going to find X

so zero is equal to x minus three

over three times X Plus 4.

just like before we're going to put this

over one and cross multiply

so we have one times x minus 3 which is

that and that's equal to zero times the

stuff on the bottom which will be zero

add in 3 to both sides we get that X is

equal to 3.

so we can write the x-intercept as three

comma zero

and so that's it for this problem so now

you know how to find the X and Y

intercepts of any rational function

pretty much you just need to follow the

procedure that you've learned in this

video and that should give you the

answer