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)