Question

What is the range of the graph for y = |x-2] + 3

Answer 1

it is easier to see this in the graph

So we can give values to X and look the graph

`\begin{gathered} x=-2\longrightarrow\text{ y=7} \\ x=-1\longrightarrow y=6 \\ x=0\longrightarrow y=5 \\ x=1\longrightarrow y=4 \\ x=2\longrightarrow y=3 \\ x=3\longrightarrow y=4 \end{gathered}`

the graph is something like this

and the range is all the values ​​it can take in Y

From the graph we observe that values ​​less than 3 will not be taken because the function is a absolute value

And it will only take values ​​greater than 3

So the range is:

`\lbrack3,\infty)`