# Lesson Worksheet: Step Functions Mathematics

In this worksheet, we will practice identifying and analyzing a step function’s domain, range, intercepts, end behavior, continuity, and decreasing and increasing intervals.

Q1:

State the domain and range of the step function whose graph is shown. • BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Q2:

State the domain and range of the following function:

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Q3:

Evaluate the following function, , for the given values of . Q4:

Find the rule of the following function. • A
• B
• C
• D
• E

Q5:

Which of the following functions is a step function?

• A • B • C • D • E Q6:

State the domain and range of the function

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Q7:

State the domain and range of the function

• BDomain: , range:
• CDomain: , range:
• DDomain: , range:
• EDomain: , range:

Q8:

Consider the following function:

If its domain is and its range is , find and .

• A,
• B,
• C,
• D,
• E,

Q9:

Find the rule for the step function whose graph is shown. • A
• B
• C
• D
• E

Q10:

The function takes a real number and rounds it down to the greatest integer less than or equal to . For example, , , and .

Noah says we can just say that the floor of is the integer part of the decimal expansion of . Is he right? If not, why?

• ANo. This is only true if . For example, the floor of 0.5 is 1, not 0.
• BNo. This is only true if . For example, the floor of 0.5 is , not 0.
• CNo. This is only true if . For example, the floor of is 0, not .
• DNo. This is only true if . For example, the floor of is , not 0.
• EYes

Define a function by . What are the values of , , , and ?

• A
• B
• C
• D
• E

Evidently, . What is the range of ?

• A
• B
• C
• D
• E

What are all the solutions to ?

• AAll the integers
• BAll the natural numbers
• CAll the integers
• DAll the integers
• EAll the numbers

The following is the graph of . Which is the graph of ? • A(d)
• B(c)
• C(a)
• D(b)