Question

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below? logarithmic graph passing through point 3, 0. f(x − 2) f(x + 2) f(x) − 2 f(x) + 2

Answer 1

Given parent function: f(x) =
`log_3 x`.

Let us find the x-intercept of the given parent function.

In order to find the x-intercept, we need to set given function equal to 0 and solve for x.

Therefore,

`log_3 x =0`

Let us convert log to exponential form, we get

`3^0 = x`

Power 0 of anything is 1.

Therefore, x=1.

So, the x-intercept of parent function is 1.

And x-intercept of the given graph is 3.

So, the given graph is being shifted 2 units right.

According to rule of transformations g(x) = f(x-k) shift k units right.

Therefore, correct option is f(x − 2).