Chapter 2, Problem 35RE

To determine

To graph: The function $h\left(x\right)={\left(x-1\right)}^2+2$, find the intercepts and state the domain and range.

Answer to Problem 35RE

Solution:

The $y\text{-intercepts}$ is $\left(0,3\right)$.

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

The range of the function is $[2,\infty )$.

Explanation of Solution

Given:

$h\left(x\right)={\left(x-1\right)}^2+2$

Graph:

Draw the graph the basic function $h\left(x\right)={\left(x-1\right)}^2$ as follows:

Now draw the graph of the function $h\left(x\right)={\left(x-1\right)}^2+2$ as follows:

Interpretation:

The final graph of the function is shifted 2 units up as compared to that of the graph of the basic function.

The $y\text{-intercepts}$ is $\left(0,3\right)$.

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

The range of the function is $[2,\infty )$.