Chapter 2, Problem 33RE

To determine

To graph: The function $h\left(x\right)=\sqrt{x-1}$, find the intercepts and state the domain and range.

Answer to Problem 33RE

Solution:

The $x\text{-intercepts}$ is $\left(1,0\right)$.

The domain of the function is $[1,\infty )$.

The range of the function is $[0,\infty )$.

Explanation of Solution

Given:

$h\left(x\right)=\sqrt{x-1}$

Graph:

Draw the graph the basic function $h\left(x\right)=\sqrt{x}$ as follows:

Now draw the graph of the function $h\left(x\right)=\sqrt{x-1}$ as follows:

Interpretation:

The final graph of the function is shifted 1 unit to the right as compared to that of the graph of the basic function.

The $x\text{-intercepts}$ is $\left(1,0\right)$.

The domain of the function is $[1,\infty )$.

The range of the function is $[0,\infty )$.