Question

Graphing Functions Graph the function in each of the given viewing rectangles, and select the one that produces the most appropriate graph of the function.

$f\left(x\right)=x^2-x-20$

(a)$[-2,2]\text{by}[-5,5]$
(b)$[-10,10]\text{by}[-10,10]$
(c)$[-7,7]\text{by}[-25,20]$
(d)$[-10,10]\text{by}[-100,100]$

Short answer

Window $\left(c\right)[-7,7]\mathrm{by}[-25,20]$produces the most appropriate graph of the function.

Step-by-step solution

Part a. Step 1. Use definition of a graph of a function.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Part a. Step 2. Analyze the information given.

We are given the following function

$\begin{array}{l}\text{Function}:f\left(x\right)=x^2-x-20\\ \text{Viewingwindow}:[-2,2]\mathrm{by}[-5,5]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values. Or we will use a graphing calculator

Part a. Step 3. Graph the function.

Next we plot these points and join the lines to get the graph of the function given as shown:

Part b. Step 1. Use definition of a graph of a function.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Part b. Step 2. Analyze the information given.

We are given the following function

$\begin{array}{l}\text{Function}:f\left(x\right)=x^2-x-20\\ \text{Viewingwindow}:[-10,10]\mathrm{by}[-10,10]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values. Or we will use a graphing calculator

Part b. Step 3. Graph the function.

Next we plot these points and join the lines to get the graph of the function given as shown:

Part c. Step 1. Use definition of a graph of a function.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Part c. Step 2. Analyze the information given.

We are given the following function

$\begin{array}{l}\text{Function}:f\left(x\right)=x^2-x-20\\ \text{Viewingwindow}:[-7,7]\mathrm{by}[-25,20]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values. Or we will use a graphing calculator

Part c. Step 3. Graph the function.

Next we plot these points and join the lines to get the graph of the function given as shown:

Part d. Step 1. Use definition of a graph of a function.

A function is defined as, given a set of inputs X and a set of possible outputs Y as a set of ordered pairs (x, y). We can write the statement that f is a function from X to Y using the function notationf: $X\to Y$.

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Part d. Step 2. Analyze the information given.

We are given the following function

$\begin{array}{l}\text{Function}:f\left(x\right)=x^2-x-20\\ \text{Viewingwindow}:[-10,10]\mathrm{by}[-100,100]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values. Or we will use a graphing calculator

Part d. Step 3. Graph the function.

Next we plot these points and join the lines to get the graph of the function given as shown:

Part d. Step 4. Evaluate the results.

Clearly all the important features of the Graph are best seen in the window $\left(c\right)[-7,7]\mathrm{by}[-25,20]$.