Question

The graph of the funxtion f(x)=|3x| is translated 4 units up. What is the equation of the transformed function

Answer 1

`g(x)=|3x|+4`

Explanation:

Let the transformed function be
`g(x)`.

Given:

The parent function given is:

`f(x)=|3x|`

Now, the above function is translated up by 4 units.

As per the rules of transformations, if a graph of a function is translated vertically up by 'C' units, then the rule for the transformation is given as:

`f(x)\rightarrow f(x)+C`

So, 4 units will be added to the given function to get the transformed function. Therefore,

`g(x)=f(x)+4\\g(x)=|3x|+4`

Hence, the transformed function of
`f(x)=|3x|` is given as
`g(x)=|3x|+4`.