Question

Consider the function f(x)=(8-x)/(x+9)+2 Algebraically determine the domain and all of the intercepts.

Answer 1

\[x + 9 \ne 0\]\[f(x) \ne -1\]

Answer 2

To find the intercepts, set f(x) = 0, then solve for x.
Then set x = 0, then solve for f(x)

Answer 3

How did you get f(x)=-1?

Answer 4

Just by looking at the function really. I know that x + 9 is in the denominator, but when you are solving for x you usually multiply both sides by x + 9 to get rid of the denominator. But if both sides of the equation have -x, then there is no solution. The only way to get -x on both sides is if f(x) = -1

Answer 5

Actually, I didn't see the + 2

Answer 6

That changes things

Answer 7

Alrighty, well I go a different answer. When I solved for x I got -26 and for the domain I got x can't equal -9 so the domain would be [(-\infty,-9)(-9,\infty)\]

Answer 8

opps \[(-\infty,-9)(-9,\infty)\]

Answer 9

You found what x cannot equal, not what f(x) cannot equal.

Answer 10

I agree that \(x \ne -9\)

Answer 11

I don't think you have to worry about what \(f(x)\) cannot equal since it doesn't ask you to find the range.

Answer 12

Your domain appears to be correct. Now if you manage to find the intercepts, then you'll be all set.

Answer 13

Because of the + 2, \(f(x) \ne 1\). You would only need to know that if you were trying to find the range.

Answer 14

Mmkay! Thanks. Now, I just gotta find the intercepts!

Answer 15

I already posted what to do to find the intercepts.

Answer 16

I know I'm solving it haha.

Answer 17

Okay, good luck.

Answer 18

I got x-intercept (-26,0)
Y- intercept (0, 26/9)

Answer 19

That appears to be correct.

Answer 20

Thanks for the help.