Question

Which of the following functions is graphed above?

Answer 1

That would be choice D

Answer 2

It's obvious from the graph that the x-intercept is (3,0).  Thus, when x=3, y=0.  We can use this fact to eliminate those of the 4 possible answers that could not be correct.  Note that log (1) = 0.

Eliminate the first answer:  log(x + 4).  Why?  Because when x=3, 
log(x + 4)=log(3 + 4)= log 7, which is NOT zero.

Elim. the second answer for the same reason.

Next, look at the third answer:  log(x + 4).  If x=3, we get log(7), which is not zero.

That leaves only the fourth answer choice.  But check that out also:

f(x) = -4log(-x + 4).  When x=3, we get f(3)= -4log(-x + 4) = -4(log[1]) = 0.  This is correct.