Chapter 2: Q6. (page 93)

Graph each function. Identify the domain and range.
$f (x) = - [[x]]$ .

Short Answer

Expert verified

The domain is all real numbers.

The range is all integers.

Step by step solution

Step-1–Range and Domain of the function.

The domain of the function is the set of all input values and range of the function is the set of all output values.

Step-2 – Determine the domain and range.

Consider the given function $f (x) = - [[x]]$

It can be observed that the domain of the function is the set of all real values because the function can take any value of x.

Here, the function is greatest integer it means it will produce only integer values.

Therefore, the range is the set of all integers.

Step-3 – Draw the table.

The symbol $[[x]]$ means the greatest integer less than or equal to $x$ .

For example: $[[[7.3]] = 7$ ,and $, [[- 1.5]] = - 2]$

Therefore, the required table is:

Step-4 – Graph the function.

The graph of the function is:

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Graph each function. Identify the domain and range.
$f (x) = - [[x]]$ .

Short Answer

Step by step solution

Step-1–Range and Domain of the function.

Step-2 – Determine the domain and range.

Step-3 – Draw the table.

Step-4 – Graph the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Geometry

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. Identify the domain and range.f(x)=-x.

Short Answer

Step by step solution

Step-1–Range and Domain of the function.

Step-2 – Determine the domain and range.

Step-3 – Draw the table.

Step-4 – Graph the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Geometry

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each function. Identify the domain and range.
$f (x) = - [[x]]$ .