SOLUTION: How do I find the y intercept, x intercept, range, and domain of the following function: f(x)=log(2)(3-x)+2 (the (2) is a base)

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Question 876082: How do I find the y intercept, x intercept, range, and domain of the following function:
f(x)=log(2)(3-x)+2 (the (2) is a base)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find the y intercept, x intercept, range, and domain of the following function:
f(x)=log(2)(3-x)+2 (the (2) is a base)
***
f(x)=%28log%283-x%29%2Flog%282%29%29%2B2
y-intercept
set x=0
log%283%29%2Flog%282%29%2B2=3.585
...
x-intercept
set y=0
0=%28log%28%283-x%29%29%2Flog%282%29%29%2B2
%28log%28%283-x%29%29%2Flog%282%29%29=-2
-2log(2)=log(3-x)
log(2^-2)=log(3-x)
log(1/2^2)=log(3-x)
log(1/4)=log(3-x)
1/4=3-x
x=11/4
range:(-∞,∞)
domain(-∞,3)