SOLUTION: which statement about the function f(X)=x-3/x+2 is true? a-its domain does not include 2 b-its domain does not include 3 c-its range does not include 1 d-its range does not

Algebra ->  Equations -> SOLUTION: which statement about the function f(X)=x-3/x+2 is true? a-its domain does not include 2 b-its domain does not include 3 c-its range does not include 1 d-its range does not       Log On


   

Question 1099212: which statement about the function f(X)=x-3/x+2 is true?
a-its domain does not include 2
b-its domain does not include 3
c-its range does not include 1
d-its range does not include -2/3
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Variable is either x or X; pick one and stay with it.
Are necessary grouping symbols missing?

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

f%28x%29=%28x-3%29%2F%28x%2B2%29

f cannot accept x at -2 because that creates denominator of 0, not acceptable here. Otherwise, domain is the set of x values system%28x%3C-2%2CAND%2Cx%3E-2%29.

Set of possible f(x) values, the range.


The graph without further trying to analyze:
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x-3%29%2F%28x%2B2%29%29

Will f ever become 1 ?

Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!

Please note the other tutor's question about whether grouping symbols should be used. The way you submitted the problem, the function is
f%28x%29+=+x-3%2Fx%2B2

I suspect that the actual function is the one she analyzed for you:
f%28x%29+=+%28x-3%29%2F%28x%2B2%29

Then, to add to what she asked at the end of her response: Is the function value ever equal to 1?

To answer that question, simply try solving the equation f(x) = 1.
%28x-3%29%2F%28x%2B2%29+=+1
x-3+=+x%2B2 [multiplying both sides by (x+2)]
-3+=+2

There is no solution to this equation; the answer is no. The function value is never equal to 1.

It does in fact get as close as you want to 1, without ever reaching 1. So the range of the function is all values except 1.

So statements a and c are true.

Statement b is false; it is easy to evaluate the function at x=3:
f%283%29+=+%283-3%29%2F%283%2B2%29+=+0%2F5+=+0

Statement d is also false. The only value not in the range of the function is 1.
You can also verify that statement d is false by solving the equation
%28x-3%29%2F%28x%2B2%29+=+2%2F3
and finding that there is a solution.