Question

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

logarithmic graph passing through point 2, 4.

f(x + 3)
f(x − 3)
f(x) + 3
f(x) − 3

Answer 1

Answer: Third Option

`f(x) +3`

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`