SOLUTION: find the domain and range of the following function f(x) = 8/X+9

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Question 262805: find the domain and range of the following function
f(x) = 8/X+9
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
assuming you mean f(x) = 8 / (x+9), then:

the domain is all real values of x except x = -9

when x = -9, then the denominator is 0 and the range is undefined.

every value in the domain must lead to one or more values in the range or the domain is not valid.

the domain of this equation is valid except at x = -9.

the range is all real values of y except 0 since y can approach 0 but will never actually be 0.

the limit of y as x approaches infinity = 0, however, so there is a horizontal asymptote at y = 0.

there is also a vertical asymptote at x = -9. as x approaches -9, the value of y approaches +/- infinity. at x = -9, the value of y is undefined.

graph of y = 8 / (x+9) is shown below:

if you draw a vertical line at x = -9, you will see that the value of y approaches it but never touches it.

if you draw a horizontal line at y = 0, you will see that the value of y approaches it but never touches it.