Question

the graph of f(x) is shown. draw the graph of the transformed function y = f(x - 2)+2 note: you must draw the entire graph before you exit the graphing tool. once youre ready to exit, just click a second time on your last point. clear all draw: polygon question help: written example message instructor post to forum submit question

Explanation:

Step1: Identify horizontal shift

The transformation $y = f(x - 2)$ shifts the graph of $y = f(x)$ 2 units to the right. For any point $(x_0,y_0)$ on $y = f(x)$, the corresponding point on $y = f(x - 2)$ is $(x_0+2,y_0)$.

Step2: Identify vertical shift

The transformation $y = f(x - 2)+2$ shifts the graph of $y = f(x - 2)$ 2 units up. So for a point $(x_1,y_1)$ on $y = f(x - 2)$, the corresponding point on $y = f(x - 2)+2$ is $(x_1,y_1 + 2)$. In terms of the original function $y = f(x)$, if a point on $y = f(x)$ is $(x_0,y_0)$, the point on $y=f(x - 2)+2$ is $(x_0 + 2,y_0+2)$.

Step3: Transform key - points

For example, if there is a vertex of the original graph of $y = f(x)$ at $(x=a,y = b)$, the vertex of the transformed graph $y = f(x - 2)+2$ will be at $(a + 2,b + 2)$. Do this for all key - points (such as vertices, intercepts) of the original graph of $y = f(x)$ and then connect the new points to draw the transformed graph.

Since this is a graph - drawing problem and we can't actually draw in this text - based format, the steps above describe how to draw the graph of $y = f(x - 2)+2$ from the graph of $y = f(x)$. The new graph is the original graph shifted 2 units to the right and 2 units up.

Answer:

Step1: Identify horizontal shift

The transformation $y = f(x - 2)$ shifts the graph of $y = f(x)$ 2 units to the right. For any point $(x_0,y_0)$ on $y = f(x)$, the corresponding point on $y = f(x - 2)$ is $(x_0+2,y_0)$.

Step2: Identify vertical shift

The transformation $y = f(x - 2)+2$ shifts the graph of $y = f(x - 2)$ 2 units up. So for a point $(x_1,y_1)$ on $y = f(x - 2)$, the corresponding point on $y = f(x - 2)+2$ is $(x_1,y_1 + 2)$. In terms of the original function $y = f(x)$, if a point on $y = f(x)$ is $(x_0,y_0)$, the point on $y=f(x - 2)+2$ is $(x_0 + 2,y_0+2)$.

Step3: Transform key - points

For example, if there is a vertex of the original graph of $y = f(x)$ at $(x=a,y = b)$, the vertex of the transformed graph $y = f(x - 2)+2$ will be at $(a + 2,b + 2)$. Do this for all key - points (such as vertices, intercepts) of the original graph of $y = f(x)$ and then connect the new points to draw the transformed graph.

Since this is a graph - drawing problem and we can't actually draw in this text - based format, the steps above describe how to draw the graph of $y = f(x - 2)+2$ from the graph of $y = f(x)$. The new graph is the original graph shifted 2 units to the right and 2 units up.