Step and Ceiling Function Concepts

This video tutorial explores the floor and ceiling functions, which are piecewise step functions. The floor function rounds down to the greatest integer less than or equal to a given number, while the ceiling function rounds up to the least integer greater than or equal to a given number. The video also covers how to evaluate these functions and discusses transformations such as vertical dilation and horizontal translation, similar to those in quadratic functions.

What is the domain of both floor and ceiling functions?

• All real numbers

• Negative integers only

• All integers

• Positive integers only

What is the range of the floor function?

• All real numbers

• Only positive integers

• Only negative integers

• Only integers

How is the floor function represented in notation?

• A curly brace

• A parenthesis

• A bracket with a floor

• A bracket with a ceiling

What does the floor function do to the number 1.5?

• Rounds to 1.5

• Rounds up to 2

• Rounds down to 1

• Rounds to 0

Where is the solid dot located in a ceiling function graph?

• There is no solid dot

• On the right side

• On the left side

• In the middle

What does the ceiling function do to the number 0.5?

• Rounds to 0.5

• Rounds up to 1

• Rounds down to 0

• Rounds to 2

How does the floor function handle negative numbers like -3.2?

• Rounds to -3

• Rounds to -3.2

• Rounds down to -4

• Rounds up to -3

How does the ceiling function handle negative numbers like -3.2?

• Rounds down to -4

• Rounds up to -3

• Rounds to -3.2

• Rounds to -2

What does the 'a' value represent in step function transformations?

• Horizontal translation

• Vertical translation

• Vertical dilation

• Horizontal dilation

What happens when the 'a' value is negative in a step function?

• Reflection across the y-axis

• Vertical translation

• No reflection

• Reflection across the x-axis