Worksheet: Step Functions

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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: −2≤𝑥<4, range: {−8,−2,6.5,4}
  • BDomain: −8<𝑥≤6.5, range: {−8,−2,6.5}
  • CDomain: −2≤𝑥<4, range: {−2,0.5,4}
  • DDomain: −8≤𝑥≤6.5, range: {−2,4}
  • EDomain: −8<𝑥≤6.5, range: {−2,0.5,4}

Q2:

State the domain and range of the following function: 𝑓(𝑥)=⎧⎪⎨⎪⎩−2,−12<𝑥≤−1112,−1<𝑥<10,1≤𝑥≤4.

  • ADomain: −12<𝑥≤4, range: −12,−1,1,112,4
  • BDomain: −2<𝑥≤112, range: {−12,−1,1,4}
  • CDomain: −2≤𝑥≤112, range: {−12,−1,1,4}
  • DDomain: −12<𝑥≤4, range: −2,112,0
  • EDomain: −12≤𝑥≤4, range: −2,112,0

Q3:

Find the rule of the following function.

  • A𝑓(𝑥)=−1,−5≤𝑥<−23,−2≤𝑥<15,1≤𝑥≤5.
  • B𝑓(𝑥)=−1,−5≤𝑥<−23,−2≤𝑥≤15,1≤𝑥≤5.
  • C𝑓(𝑥)=−1,−5≤𝑥≤−23,−2<𝑥≤15,1≤𝑥≤5.
  • D𝑓(𝑥)=−1,−5≤𝑥≤−23,−2≤𝑥≤15,1≤𝑥≤5.
  • 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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