# 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.

**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

- ADomain: , range:
- BDomain: , range:
- CDomain: , range:
- DDomain: , range:
- EDomain: , range:

**Q7: **

State the domain and range of the function

- ADomain: , range:
- 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)