Question

For the function $f\left(x\right)=\sqrt{x-2}$. Find the (a) domain of the function (b) graph the function (c) use the graph to determine the range.

Short answer

The domain of the function is$[2,\infty )$and range is$[0,\infty )$

Step-by-step solution

Step 1. Given Information

$f\left(x\right)=\sqrt{x-2}$

Part (a) Step 1. Domain of the function 

We set $x-2\ge 0$and solve$x\ge 2$

Part (b) Step 1. Graph of the function 

To graph the function, we choose points in the interval $[2,\infty )$that will also give us a radicand which will be easy to take the square root.

Part (c) Step 1. Finding Range from the graph 

Looking at the graph, we see the y-values of the function are greater than or equal to zero. The range then$[0,\infty )$