Which of the following functions would result in a graph that shifted two units to the left of g(x) = 3 log (x)

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virtuematane virtuematane · Answer 1 · 2019-05-17T08:13:42+02:00

Option: C is the correct answer.

The transformed function is:

C) [tex]f(x)=3\log (x+2)[/tex]

We are given a parent function g(x) as:

[tex]g(x)=3\log x[/tex]

Now this parent function g(x) is transformed as:

It is shifted two units to the left.

( We know that when any function f(x) is shifted 'a' units to the left or right then the transformed function is: f(x+a)

if a<0 then the shift is a units to the right.

when a>0 then the shift is a units to the left )

Hence, the rule that follows this transformation is:

g(x) → g(x+2)=f(x)

Hence, the transformed function is:

[tex]f(x)=3\log (x+2)[/tex]

joaobezerra joaobezerra · Answer 2 · 2022-05-25T11:48:17+02:00

Using translation concepts, the function that would result in a graph that shifted two units to the left of g(x) = 3 log (x) is given by:

C. [tex]f(x) = 3\log{(x + 2)}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

A shift of two units to the left means that x -> x + 2 in the domain of the function, hence:

[tex]f(x) = g(x + 2) = 3\log{(x + 2)}[/tex]

Which means that option C is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517

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