Chapter 2, Problem 34RE

To determine

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

Answer to Problem 34RE

Solution:

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

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

The domain of the function is $(-\infty ,1]$.

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

Explanation of Solution

Given:

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

Graph:

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

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

Interpretation:

The final graph of the function is reflected and 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 $y\text{-intercepts}$ is $\left(0,1\right)$.

The domain of the function is $(-\infty ,1]$.

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