Question

x and y intercept of ((x+1)^3 / (x-1)^2) Please!...i know that x-intercept is x=0 and y-intercept is f(0)....y-intercept result is 1 (i think)...now I have to look for the x-intercept...this is where I need help :/

Answer 1

\[f(x) = ((x+1)^3 / (x-1)^2) = 0\]
f(x) is undefined when :
\[(x−1)^2 = 0 <=> x=1\]
thus:
\[(x+1)^3 = 0, x \neq1\]
\[x=-1\]

Answer 2

another way of thinking of it...instead of thinking of x and y intercepts...you are finding out where the equation crosses with the lines y=0(is the line that is the x axis) and x=0(which makes a line on the y axis) by plugging in those values into the equation..you are simpliy figuring out where it touches on those lines

Answer 3

so the x-intercept is x=-1?

Answer 4

exactly.

Answer 5

actually when talking about an intercept, we're talking about a point. So the intercept is (-1, 0).

Answer 6

so, I only have to look the value where (in this case) the denominator = 0...so that value is the x-intercept?

Answer 7

the value that make the denominator = 0 is the x-intercept?

Answer 8

no. you just need to check that the denominator isn't 0 so you can just look at the numerator.

Answer 9

as long as the numerator is 0, the whole fraction is 0, unless the denominator is 0 in which case the fraction doesn't exist.

Answer 10

0/x = 0, x != 0

Answer 11

ok...and in this exercise?? e^-x sen(x)

Answer 12

(e^-x)(sen x)...find the x and y intercept

Answer 13

I have that the y-intercept is 0...but I'm confused about the x-intercept

Answer 14

you get two equations.
e^-x = 0 or sin(x) = 0

Answer 15

then combine the answers.

Answer 16

what do you mean by combine the answers?

Answer 17

I know that sin(x)= 0 on every pi

Answer 18

but, when e^-x=0??

Answer 19

well from sin(x) = 0 you get PI*n, n is Z
and from e^-x you don't get a zero

Answer 20

so..it doesn't have x-intercepts?

Answer 21

the answer is
\[\pi*n, n \in Z\]

Answer 22

no, e^-x doesn't have x-intercepts

Answer 23

wait...you told me that the answer is pi n and then that it doesn't have x-intercepts :/

Answer 24

the problem is (e^-x)(sen x)

Answer 25

to the whole problem the answer is PI n

Answer 26

oh okay

Answer 27

this is called the zero-product property

Answer 28

okay

Answer 29

could yo verify this intercepts please?

Answer 30

a. (x^2-16)/(x^2-4x) [x=>-4 and 4][y=>0]
b. (x)/(x^2 -9) [x=>0][y=>0]
c. (x)/(squared root x^2 +6) [x=>0][y=>0]
d. (sin x)/(1+cos x) [x=>pi n][y=>0]
e. (e^-x)(sen x) [x=>pi n][y=>0]
f. (x+1)^3 / (x-1)^2 [x=>-1][y=>1]

Answer 31

you can verify these yourself. just plug the answer to the expression.

Answer 32

what result do I have to get so i Know that my result is right?

Answer 33

if you plug the x-intercept, you need to get 0 as the result.
if you plug the y-intercept (x=0), you need to get the answer as the result.

Answer 34

thank you A LOT!