Question

Graph the function $y=\sqrt{x}-1$ and then state the domain and range of the function.

Short answer

The graph of the function $y=\sqrt{x}-1$is shown below whose domain is $\left[0,\infty \right)$and range is$\left[-1,\infty \right)$.

Step-by-step solution

Step 1. Write down the given information.

The given function is $y=\sqrt{x}-1$.

Step 2. Sketch the graph of given function.

The graph of the function$y=\sqrt{x}-1$ is shown below.

Step 3. Interpretation from the graph.

From the graph, it can be interpreted that the domain of the function$y=\sqrt{x}-1$is $x\ge 0$ and range is $y\ge -1$.

Mathematically, domain $D_f\in \left[0,\infty \right)$and range $R_f\in \left[-1,\infty \right)$of the function$y=\sqrt{x}-1$ .