Question

Given the parent function f(x) what is the equation of the function shown in the graph?

Answer 1

I'm guessing you're looking for something \[\Large f(x) = a \log_2 (x-h) +k\]

Answer 2

yes lol @agent0smith

Answer 3

h is easy, the horizontal shift is 4 to the left so \[\Large f(x) = a \log_2 (x+4) +k\]Now you can plug in the other points to find k and a
Notice when x=-3, y=-1
\[\Large -1 = a \log_2 (-3+4) +k\] \[\Large -1 = a \log_2 (1) +k\] log1 is equal to zero, so \[\Large -1 =k\]

Answer 4

Now you could plug in another point like (4, 2) to find a

Answer 5

i think i got lost lol

Answer 6

The normal asymptote for a log function is x=0, this is x=-4, so a shift 4 to the left means h=-4

Answer 7

2 = alog2 (4+4) + k

Answer 8

Yes, no solve that for a... you know k=-1 from above btw.

Answer 9

*now

Answer 10

f(x) = log2(x + 4) - 1

Answer 11

2 = a log2 (4+4) - 1

solve for a by simplifying