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.

$f\left(x\right)=x^3-5x-4$

(a)$[-2,2]\text{by}[-2,2]$
(b)$[-3,3]\text{by}[-10,10]$
(c)$[-3,3]\text{by}[-10,5]$
(d)$[-10,10]\text{by}[-10,10]$

Short answer

Window $\left(c\right)[-3,3]by[-10,5]$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

$\begin{array}{l}f\left(x\right)=x^3-5x-4\\ \left(a\right)[-2,2]by[-2,2]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values.

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

$\begin{array}{l}f\left(x\right)=x^3-5x-4\\ \left(b\right)[-3,3]by[-10,10]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values.

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

$\begin{array}{l}f\left(x\right)=x^3-5x-4\\ \left(c\right)[-3,3]by[-10,5]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values.

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

$\begin{array}{l}f\left(x\right)=x^3-5x-4\\ \left(d\right)[-10,10]by[-10,10]\end{array}$

To graph this function we choose random x-values and plug then in the function to get the y-values.

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 $\left(c\right)[-3,3]by[-10,5]$.