Chapter 3.3, Problem 69AYU

In Problems 63-74, (a) graph each function, (b) determine the domain and the range of the function, and (c) determine where the function is increasing and where it is decreasing.

$f\left(x\right)=2x^2+x+1$

To determine

To calculate:

1. Graph the given function.
2. Determine the domain and range of the given function.
3. Determine where the function is increasing and where it is decreasing.

Answer to Problem 69AYU

1. The graph of the function is given below.

2. The domain of the given function is the set of all real numbers and the range of the given function is $[0.875,\infty )$.
3. The function is increasing in the interval $[-0.25,\infty )$ and decreasing in the interval $(-\infty ,-0.25]$

Explanation of Solution

Given:

The given function is $f(x)=2x^2+x+1$.

Formula Used:

Domain is the set of all possible values that $x$ can take.

Range is the possible results for any values of $x$.

Calculation:

a. The graph of the given function is

b. From the above graph, we can see that the domain of the function is the set of all real numbers. The range of the function is also $[0.875,\infty )$.

c. The function is increasing in the interval $[-0.25,\infty )$ and is decreasing in the interval $(-\infty ,-0.25]$.