Question

Sketch the graph of the function. $$ g(x)=\llbracket x+1 \rrbracket $$

   Sketch the graph of the function.
$$
g(x)=\llbracket x+1 \rrbracket
$$

Precalculus: A Concise Course

Precalculus: A Concise Course

Ron Larson, David C.… 2nd Edition

Chapter 1, Problem 55

Instant Answer

Solved by Expert James Kiss

07/26/2021

Step 1

This is the greatest integer function, also known as the floor function. It rounds down a real number to the largest integer less than or equal to that number. Show more…

Show all steps

lock

Thanks for your feedback!

Sketch the graph of the function. $$ g(x)=\llbracket x+1 \rrbracket $$

Play audio

Feedback

Powered by NumerAI

James Kiss and 80 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Floor Function

The floor function assigns to any real number the greatest integer less than or equal to that number. It is inherently step-like, as its value remains constant over an interval until the next integer is reached, leading to sudden jumps in the graph.

Translation of Functions

Translating a function involves shifting its graph horizontally or vertically. In the case of a function like g(x) = [x+1], the addition inside the function's argument causes a horizontal shift, moving the behavior and discontinuities of the floor function along the x-axis.

Piecewise Constant Functions

A piecewise constant function is one that takes on constant values over intervals separated by jumps or discontinuities. This type of function, exemplified by the floor function, has a graph composed of discrete, horizontal segments.

Discontinuities

Discontinuities in a function refer to points where the function suddenly changes value, often creating breaks in the graph. In step functions such as the floor function, these occur at the endpoints of the constant intervals, where the function value jumps to a new level.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later