Question

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

A) f(x − 2)
B) f(x + 2)
C) f(x) − 2
D) f(x) + 2

Answer 1

Answer : option B

Parent Graph f(x) =
`log_3(x)` is attached below

We analyze each option

A) f(x − 2) --> x - 2 shifts the graph 2 units to the right

B) f(x + 2) --> x + 2 shifts the graph 2 units to the left

C) f(x) − 2 --> f(x) - 2 shifts the graph 2 units down

D) f(x) + 2 --> f(x) + 2 shifts the graph 2 units up

In the graph of f(x)=
`log_3(x)` , the x intercept at x=1

From the graph attached in the question, the x intercept at x=-1

Its means the parent graph is shifted 2 units to the left.

Option B: f(x + 2) --> x + 2 shifts the graph 2 units to the left