ANSWER and EXPLANATION
a) We want to graph the function given:
[tex]y=|x-3|[/tex]
To do this, we have to pick some values of x and find the corresponding values of y.
Let us find y when x is 2, 3, and 4.
[tex]\begin{gathered} \Rightarrow x=2\colon \\ y=|2-3|=|-1| \\ y=1 \\ \Rightarrow x=3\colon \\ y=|3-3|=|0| \\ y=0 \\ \Rightarrow x=4\colon \\ y=|4-3|=|1| \\ y=1 \end{gathered}[/tex]
Now, we have coordinate points to plot with:
[tex](2,1);(3,0);(4,1)[/tex]
Let us plot the graph:
b) The graph of y = |x - 3| is plotted in red while the graph of y = |x| is given in black.
As we can see, the graph of y = |x - 3| is translated on the x-axis by +3 units.
In other words, y = |x - 3| shifted 3 units to the right of y = |x|.
