Expert: Steve Holleran - 7/12/2008

Question
Hey, I'm having a hard time trying to figure out how to graph this problem, could you help me, please?

f(x)=(4/3)log(base4)of(x-3)-4

Thanks for your time

Answer
Hi Mellie,

It's understandable that you're having some trouble here, because these log functions are not easy to graph.

Basically what you have is a base 4 log graph which has had several transformations done to it.  

To start with, a basic graph of y = log,4,(x) is like any other log graph: it is vertically asymptotic to the negative y-axis in quadrant 4, passes through the x-axis at (1,0), then continues to rise (but not quickly) and stay concave down.  (See if you can find this basic graph on some math sites--shouldn't be too hard).

Then, here's what the transformations do:

the (x - 3) shifts the basic graph 3 units right (so now it would cross the x-axis at (4,0).)

the 4/3 multiplier in the front vertically "stretches" the graph a little bit, because it multiplies all the y-values by 1 1/3.  The shape is just a little "steeper".

the -4 at the end slides the whole graph down 4 units (so now the former x-intercept at (4,0) should be at (4,-4).

Without being able to draw a picture, that's about the best I can do here.  Hope it helps.

Steve