Chapter 3: Q 528. (page 362)

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.
$f (x) = x^{3} - 2$

Short Answer

Expert verified

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

The graph of the function is shown below:

Step by step solution

Step 1. Write the given information and draw the table for different x values.

The given function is $f (x) = x^{3} - 2$ .

Put the different values of $x$ into the given function and make the table as shown:

$x$	localid="1644303084951" $f (x) = y$	$(x, y)$
$0$	localid="1644303091010" $y = 0^{3} - 2 = - 2$	$(0, - 2)$
$- 1$	localid="1644303102049" $y = {(- 1)}^{3} - 2 = - 3$	$(- 1, - 3)$
$1$	localid="1644303110919" $y = 1^{3} - 2 = - 1$	$(1, - 1)$
localid="1644302789667" $- 2$	localid="1644303120878" $y = {(- 2)}^{3} - 2 = - 10$	$(- 2, - 10)$
localid="1644302799560" $2$	$y = 2^{3} - 2 = 6$	$(2, 6)$

Step 2. Draw the graph by using the obtained table.

The required graph is shown below:

Step 3. Determine the domain and range.

The domain of a function is the set of values for which the function is defined, and range is the set of all values which a function can produce.

From the graph, it can be observed that the function is defined for all real numbers and produce all real values.

Thus, the domain of the function is $(- \infty, \infty)$ and range is $(- \infty, \infty)$ .

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In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.
$f (x) = x^{3} - 2$

Short Answer

Step by step solution

Step 1. Write the given information and draw the table for different x values.

Step 2. Draw the graph by using the obtained table.

Step 3. Determine the domain and range.

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In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation. f(x)=x3-2

Short Answer

Step by step solution

Step 1. Write the given information and draw the table for different x values.

Step 2. Draw the graph by using the obtained table.

Step 3. Determine the domain and range.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Applied Mathematics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.
$f (x) = x^{3} - 2$