+1995 Given the parent function g(x)=log2x .
What is the equation of the function shown in the graph?
f(x)=log2(x−4)−2
f(x)=log2(x)−2
f(x)=log2(x+3)+4
f(x)=log2(x−3)−2
I tried figuring it out,i think it is B?
+129852 In y = log ( x - a) + b
The ( x -a) part translates the graph left/right and the "b" translates it up/down
(x - a) translates the graph right by a units
( x + a) translates the graph left by a units
+ b translates the graph up by b units
- b translates the graph down by b units
Notice that it appears the the parent has been translated to the right by 3 units...
The thing that translates the parent to the right by 3 units must be " ( x - 3 ) "
So...it appears that the last answer is correct
To check this....note that (7,0) is on the graph...which means that
0 = log2 ( 7 - 3) - 2 must be true....so....
0 = log 2 ( 4) - 2 [ Note that log2 (4) = log 4 / log 2 = 2 ]
0 = 2 - 2
Which is true !!!!
Does this make sense ???
+1995 Yes that all makes sense. I have a question though, when we go to check it we can use any point which in this case would be (7,0) or (4,-2) to check the answer? If not, why would it only be (7,0)?
+129852
Good question !!!!....note that....
Every point on the graph should check...let's check ( 4 , -2)
So we have
-2 = log2 (4 - 3) - 2 add to to both sides
0 = log2 (1) ...... [ Note log a (1) always = 0 ] [ proof...check this log (1) / log (2) ]
0 = 0
True !!!!
So...we know we have the correct equation
+1995 Awesome! Thank you for your explanation it has really helped me. 
I have been wrtiing down everything so I remember .
