Step Functions

Front

What is a step function?

Back

A step function is a piecewise constant function that jumps from one value to another without taking on any values in between.

Front

What does the ceiling function \( \lceil x \rceil \) represent?

Back

The ceiling function \( \lceil x \rceil \) rounds a number up to the nearest integer.

Front

What does the floor function \( \lfloor x \rfloor \) represent?

Back

The floor function \( \lfloor x \rfloor \) rounds a number down to the nearest integer.

Front

Calculate \( \lceil 5.7 \rceil \).

Back

6

Front

Calculate \( \lfloor -2.3 \rfloor \).

Back

-3

Front

What is the value of y when x = 1 in the step function defined as y = 2 for 0 ≤ x < 2?

Back

2

Front

What is the value of y when x = 3 in the step function defined as y = 4 for 2 ≤ x < 4?

Back

4

Front

If a step function has a value of 5 for 0 ≤ x < 1, what is the value of the function at x = 0.5?

Back

5

Front

If a step function has a value of 3 for 1 ≤ x < 2, what is the value of the function at x = 1.5?

Back

3

Front

What is the range of the step function defined as y = 1 for 0 ≤ x < 1 and y = 2 for 1 ≤ x < 2?

Back

The range is {1, 2}.