Worksheet: Step Functions

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.

  • ADomain: 2𝑥<4, range: {8,2,6.5,4}
  • BDomain: 8<𝑥6.5, range: {8,2,6.5}
  • CDomain: 2𝑥<4, range: {2,0.5,4}
  • DDomain: 8𝑥6.5, range: {2,4}
  • EDomain: 8<𝑥6.5, range: {2,0.5,4}

Q2:

State the domain and range of the following function: 𝑓(𝑥)=2,12<𝑥1112,1<𝑥<10,1𝑥4.

  • ADomain: 12<𝑥4, range: 12,1,1,112,4
  • BDomain: 2<𝑥112, range: {12,1,1,4}
  • CDomain: 2𝑥112, range: {12,1,1,4}
  • DDomain: 12<𝑥4, range: 2,112,0
  • EDomain: 12𝑥4, range: 2,112,0

Q3:

Find the rule of the following function.

  • A𝑓(𝑥)=1,5𝑥<23,2𝑥<15,1𝑥5.
  • B𝑓(𝑥)=1,5𝑥<23,2𝑥15,1𝑥5.
  • C𝑓(𝑥)=1,5𝑥23,2<𝑥15,1𝑥5.
  • D𝑓(𝑥)=1,5𝑥23,2𝑥15,1𝑥5.
  • E𝑓(𝑥)=1,5<𝑥<23,2<𝑥<15,1<𝑥<5.

Q4:

Evaluate the following function, 𝑓, for the given values of 𝑥.

𝑓(3)

𝑓(2)

𝑓(0)

Q5:

Which of the following functions is a step function?

  • A
  • B
  • C
  • D
  • E

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