Question

I need to find the domain and range, the x and y intercepts and the horizontal asymptote, then I need to graph it


f(x) =2/x^2-2x-3

Answer 1

the entire denominator is x^2 - 2x - 3 right?

Answer 2

Yes!

Answer 3

ok thanks

Answer 4

The denominator can't be zero (since you cannot divide by zero), if it were, then...

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x-3 = 0 or x+1 = 0

x = 3 or x = -1

Answer 5

So the values x = 3 or x = -1 make the denominator zero

This means that we must pull these values from the domain

Answer 6

This also means that the two vertical asymptotes are x = 3 and x = -1

Answer 7

The horizontal asymptote is y = 0 because the degree of the denominator is larger than the degree of the numerator

Answer 8

To find the x-intercept, you plug in y = 0 and solve for x

To find the y-intercept, you plug in x = 0 and solve for y

Answer 9

Wouldn't they be the same then?

Answer 10

no not always

Answer 11

they're only the same if the graph goes through the origin

Answer 12

Okay, I'm sorry I don't know how I plug them in, well where, I have to teach myself everything the class is online..

Answer 13

Do I plug 0 into the original problem?

Answer 14

there's no teacher? that's stupid

Answer 15

x-intercept

y =2/(x^2-2x-3)

0 =2/(x^2-2x-3) .. plug in y = 0 and solve for x

0(x^2-2x-3) = 2

0 = 2

this is FALSE, so there are no solutions to this particular equation

this means that there are no x-intercepts

Answer 16

It's an online class, It's basically a long page I read and am supposed to understand...

Answer 17

y-intercept

y =2/(x^2-2x-3)

y =2/((0)^2-2(0)-3) ... plug in x = 0 and solve for y

y =2/(0 - 0 -3)

y =2/(-3)

y = -2/3

So the y-intercept is (0, -2/3)

Answer 18

i see

Answer 19

Okay, thanks:) That very helpful, now I have one more question...How do I find the domain and range?

Answer 20

well the domain is the set of all real numbers BUT x cannot be 3 and x cannot be -1

remember how these values make the denominator zero, which isn't allowed

every other x value works for the domain though

Answer 21

this is shown above when I found the vertical asymptotes

Answer 22

the range is the set of all real numbers BUT y cannot be equal to 0 because this is the horizontal asymptote

Answer 23

Oh, Okay thanks much:)

Answer 24

yw