Question

how do you find the x and y intercepts of g(x)= (x^2)/(x^2-4)

Answer 1

x=0, g(x)=y=0

Answer 2

how do you get that without a calculator

Answer 3

Remember, the y intercept is just g(0), so evaluate that, no calculator needed!

To get the x intercept, you just need to find a value of x that will make \[\frac{x^2}{x^2-4}=0\]Can you see how that might be done?

Answer 4

Hint: sometimes the x intercept and the y intercept might have the same value :-)

Answer 5

why isnt the x intercept -4

Answer 6

i mean y intercept

Answer 7

y intercept means x=0; the whole equation will be: 0/0-4, which is 0

Answer 8

so if an equation has a 0 in the numerator its automatically 0?

Answer 9

As long as there isn't also a 0 in the denominator...

Answer 10

okay that makes sense

Answer 11

Divide 0 by any number other than 0 and you always get 0, right?

Answer 12

right

Answer 13

and can you explain further how to get the x intercept

Answer 14

And there is no other number that you can divide by any number to get 0. You can get really close if you divide by a really big number, but that's still infinitely far away from 0

Answer 15

The x intercept is just the place (or places) where the function crosses the x-axis — in other words, the value of the function = 0. So, we have to solve g(x) = 0. In this case, it's clear that the only way to get g(x) = 0 is at x = 0, which happens to be the y intercept as well.

Answer 16

but how do you know 0 is how you solve the function

Answer 17

It's really easy if the equation is just a line like y = mx + b. 0 = mx + b, x = -b/m giving you an x-intercept of -b/m (and the y-intercept is just b).

Answer 18

The line crosses the x-axis at points where y = 0, right? Isn't that the definition of the x-axis, the line where y = 0? Similarly, the y axis is all points where x = 0?

Answer 19

im lost

Answer 20

what do you have to do, to get x by itself