Question

All of the answers on the picture, with work provided

Answer 1

ANSWER and EXPLANATION

a) We want to graph the function given:

`y=|x-3|`

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.

`\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}`

Now, we have coordinate points to plot with:

`(2,1);(3,0);(4,1)`

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|.