Question 407632
{{{f(x)= 3+log(2, (-x))}}}<br>
The parent function is
{{{q(x) = log(2, (x))}}}
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.)<br>
I'll do one to get you started:
x = 1/2
Since {{{2^(-1) = 1/2}}}, {{{log(2, (1/2)) = -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.<br>
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.