What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

f(x − 2)
f(x + 2)
f(x) − 2
f(x) + 2

Question

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

 f(x − 2)
 f(x + 2)
 f(x) − 2
 f(x) + 2

anonymous · Answer

attachment

solomonzelman · Answer

In a case of,

$\large\color{#000000 }{ \displaystyle y=\log(ax) }$


you use, `log(a•b)=log(a)+log(a)`
So your function reallly says:

$\large\color{#000000 }{ \displaystyle y=\log(a)+\log(x) }$

solomonzelman · Answer

So it is a vertical shift ((the log(a) is a constant like any other))

anonymous · Answer

@SolomonZelman I'm still confused

solomonzelman · Answer

Oh, I am sorry, the parent function they set is log(3x), which is a little wierd.

solomonzelman · Answer

But the shift is not 2...

solomonzelman · Answer

In any case, though, you can at least determine the direction of the shift. Parent function https://www.desmos.com/calculator/brehcnexdc Your function https://www.desmos.com/calculator/sas4zak1ou

solomonzelman · Answer

So I will give it away because none of the answers are right.

the shift is actually   f(x+4/3)

anonymous · Answer

So if none of the answers match the actual shift, what do I do? @SolomonZelman

solomonzelman · Answer

the closest is f(x+2)