Question

Use transformations to graph the equation$y=\left|x-3\right|+2$.

Short answer

The graph is

Step-by-step solution

Step 1. Given Information

We are given the equation $y=\left|x-3\right|+2$and we need to use transformations to graph it.

Step 2. Using transformations

From the concept of the vertical and horizontal shift we know, the graph of $g\left(x\right)=f(x+c)+k$will be the graph of $f\left(x\right)$shifted left or right by $c$units depending upon the sign and up or down by $k$units depending upon the sign.

The equation can be written as:

$$\begin{gathered} y=\left|x-3\right|+2 \\ \Rightarrow y-2=\left|x-3\right| \end{gathered}$$

Let $$\begin{gathered} X\equiv x-3 \\ Y\equiv y-2 \end{gathered}$$

The lines pass through $X=0,Y=0$.

$$\begin{gathered} \therefore x-3=0 \\ \Rightarrow x=3 \\ y-2=0 \\ \Rightarrow y=2 \end{gathered}$$

Step 3. Plotting the graph

The graph of the equation is