Question

State the domain of the rational function.
f(x) = 16/(13-x)

Answer 1

the domain are all "valid x values"

"non-valid" or "bad" x values are those that cause you to divide by 0, or take the square root of a negative number.

In this case, there is only 1 bad x value. can you name it ?
you would say the domain is
x is all real numbers, except x≠ (fill in the bad x)

Answer 2

16?

Answer 3

what is the denominator of 16/(13-x) when x is 16 ?

Answer 4

in other words, what is 13-x when x is 16 ?

Answer 5

-3

Answer 6

and that is not zero, so x=16 is ok. you would get f(16)= 16/-3 which is a number
a bad x would cause you to do f(?)= 16/0 and dividing by 0 is bad. The result is undefined.

what x would make 13-x zero?

you could use algebra and solve for
13-x =0
add x to both sides to solve
13-x+x = 0+x
simplify
what do you get ?

Answer 7

13

Answer 8

yes, so you want to say the domain for your function is
all real numbers, but x ≠ 13

Answer 9

oh, Okay thanks:)