Finding domain/ x-y intercepts from functions :/

[A_Munk3y]

Homework Statement

I know that this prob isn't calc, but I'm learning it in calc class now so i thought it would go here :)
Anyways, these 3 functions
y=1/(x²
y=(x+4)^-2
y=1/(x²-x-2)

The Attempt at a Solution

for this,
y=1/(x²
the domain is (-infinity,0)U(0,infinity)
x-intercept; set y=0, so 0=1/x³ 0*x³=1 x=0?
y-intercept; set x=0, so y=1/0 so y=0?

y=(x+4)^-2
domain is (-infinity,-4)U(-4,infinity)
x-int; set y=0, so 0=1/(x+4)² 0=1, so x=0
y-int; set x=0, so y=1/4² so y=1/16?

y=1/(x²-x-2)
=> y=1/(x+1)(x-2)
Domain is (-infinity,-1)U(-1,2)U(2,infinity)
y-int; set x=0, so y=1/(1*-2 y=(-1/2)
x-int; set y=0 so 0=1/(x+1)(x+2) 0*(x+1)(x+2)=1 so x=0?? that makes no sense, so this gives me the idea that I'm trying to get the x and y intercepts wrong

so what am i doing wrong here?

 

[HallsofIvy]

Homework Statement

I know that this prob isn't calc, but I'm learning it in calc class now so i thought it would go here :)
Anyways, these 3 functions
y=1/(x²
y=(x+4)^-2
y=1/(x²-x-2)

The Attempt at a Solution

for this,
y=1/(x²
the domain is (-infinity,0)U(0,infinity)

Yes, x can be any number except 0.

x-intercept; set y=0, so 0=1/x³ 0*x³=1 x=0?

NO. If x= 0, then your equation becomes 0*0= 1 which is NOT true. 0*x= 1 is not true for any x. There is no x-intercept.

y-intercept; set x=0, so y=1/0 so y=0?

I have a bad feeling here. You are taking a Calculus course but are posting algebra problems that you can't do- and you apparently can't do them because you can't do arithmetic- 1/0 is NOT 0, it is not defined. There is NO y- intercept.

y=(x+4)^-2
domain is (-infinity,-4)U(-4,infinity)

Good. x can be any number except -4.

x-int; set y=0, so 0=1/(x+4)² 0=1, so x=0

Again, no. 0 is NOT equal to 1 and x= 0 gives 16(0)= 1 which is not true- 16(0)= 0. There is no x-intercept.

y-int; set x=0, so y=1/4² so y=1/16?

Yes, that is correct.

y=1/(x²-x-2)
=> y=1/(x+1)(x-2)
Domain is (-infinity,-1)U(-1,2)U(2,infinity)

Good! x can be any number except -1 and 2.

y-int; set x=0, so y=1/(1*-2 y=(-1/2)

Yes, that is correct.

x-int; set y=0 so 0=1/(x+1)(x+2) 0*(x+1)(x+2)=1 so x=0?? that makes no sense, so this gives me the idea that I'm trying to get the x and y intercepts wrong

so what am i doing wrong here?

You seem, to be under the impression that 0*x will be equal to 1 when x= 0. That is not true. 0*x= 0 whatever x is. There is NO value of x that will make 0*x= 1. There is no x-intercept. (A general arithmetic rule: a fraction is equal to 0 if and only if its numerator is 0. Its denominator plays no part in that at all.)