Chapter 4.7, Problem 9E

To determine

To match: the function $y=f\left(x-2\right)+2$ with the appropriate transformation of the graph of $y=f\left(x\right)$ .

Answer to Problem 9E

The function $y=f\left(x-2\right)+2$ matches with graph D.

Explanation of Solution

Given information:

Graph of given function,

  

Transformed graphs are given as

  

Concept used:

The graph of $y=f\left(x-h\right)+k$ can be found by translating the graph of $y=f\left(x\right)$ by $k$ units up vertically and $h$ units right horizontally.

Calculation:

Consider the given graph.

  

The function $y=f\left(x-2\right)+2$ is of the form $y=f\left(x-h\right)+k$ where $h=2,k=2$ .

So, the graph of $y=f\left(x-2\right)+2$ can be found by translating the graph of $y=f\left(x\right)$ by $2$ units right horizontally and 2 units up vertically.

So, the transformed graph will be shown as

  

Hence, the correct transformation is D.