SOLUTION: name the parent function; list 3 points that exist on the graph of the parent function; and describe the transformations needed to obtain the given function; f(x)= 3+log base 2 o

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: name the parent function; list 3 points that exist on the graph of the parent function; and describe the transformations needed to obtain the given function; f(x)= 3+log base 2 o      Log On


   

Question 407632: name the parent function; list 3 points that exist on the graph of the parent function; and describe the transformations needed to obtain the given function;
f(x)= 3+log base 2 of (-x)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+3%2Blog%282%2C+%28-x%29%29

The parent function is
q%28x%29+=+log%282%2C+%28x%29%29
For the three points we pick values and find the y values. Since our calculators do not have a button for base 2 logarithms, we will be clever and pick x values that are powers of 2. This will allow us to find the logarithms without having to change the base (so we could use our calculators.)

I'll do one to get you started:
x = 1/2
Since 2%5E%28-1%29+=+1%2F2, log%282%2C+%281%2F2%29%29+=+-1. So the point (1/2, -1) is on the graph of q(x). I'll leave it up to you to to pick other powers of 2 for x and to find their y values.

There are two transformations from q(x) to f(x). The minus in front of x will cause the graph of f to be a reflection of the graph of q in the y-axis. The "2+" will cause the graph of f to be translated three units up from the graph of q.