Question

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

Answer 1

Answer: Third Option

$f(x) +3$

Step-by-step explanation:

The function $y=log_2(x)$ passes through point (2, 1) because the exponential function $2 ^ x = 2$ when $x = 1$.

Then, if the transformed function passes through point (2, 4) then this means that the graph of $y=log_2(x)$ was moved vertically 3 units up.

The transformation that vertically displaces the graph of a function k units upwards is:

$y = f (x) + k$

Where k is a positive number. In this case $k = 3$

Then the transformation is:

$f(x) +3$

and the transformed function is:

$y = log_2 (x) +3$