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.

  • 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

Q6:

State the domain and range of the function 𝑓(𝑥)=−3,−5<𝑥≤1,4,1<𝑥<4,6,4≤𝑥<8.

  • ADomain: [−3,6), range: {−3,4,8}
  • BDomain: (−5,8], range: {−3,4,6}
  • CDomain: [−5,8), range: {−3,1,6}
  • DDomain: (−5,8), range: {−3,4,6}
  • EDomain: [−3,6], range: {−5,4,8}

Q7:

State the domain and range of the function 𝑓(𝑥)=8,−11≤𝑥<−8,4,−8<𝑥<−2,−2,−2≤𝑥<7.

  • ADomain: [−11,7]−{−8}, range: {−11,−8,7}
  • BDomain: (−11,7)−{−2}, range: {8,4,−2}
  • CDomain: [−11,7)−{−8}, range: {8,4,−2}
  • DDomain: (−11,7]−{−8}, range: {8,−8,−2}
  • EDomain: [−11,7]−{−2}, range: {8,4,−2}

Q8:

Consider the following function:

𝑓(𝑥)=⎧⎪⎨⎪⎩7,𝑎≤𝑥<−1,𝑏,−1≤𝑥<3,−4,3≤𝑥<7.

If its domain is −5≤𝑥<7 and its range is {−4,2,7}, find 𝑎 and 𝑏.

  • A𝑎=−5, 𝑏=2
  • B𝑎=−4, 𝑏=2
  • C𝑎=−5, 𝑏=3
  • D𝑎=2, 𝑏=3
  • E𝑎=2, 𝑏=−5

Q9:

Find the rule for the step function whose graph is shown.

  • A𝑓(𝑥)=⎧⎪⎨⎪⎩9,−10<𝑥≤−5,5,−5<𝑥<−3,−5,−3<𝑥<2,3,2<𝑥≤4
  • B𝑓(𝑥)=⎧⎪⎨⎪⎩9,−10<𝑥≤−5,5,−5<𝑥<−3,−5,−3≤𝑥<2,3,2<𝑥<4
  • C𝑓(𝑥)=⎧⎪⎨⎪⎩9,−10<𝑥≤−5,5,−5<𝑥<−3,−5,−3≤𝑥<2,3,2<𝑥≤4
  • D𝑓(𝑥)=⎧⎪⎨⎪⎩9,−10<𝑥<−5,5,−5<𝑥<−3,−5,−3≤𝑥<2,3,2<𝑥≤4
  • E𝑓(𝑥)=⎧⎪⎨⎪⎩9,−10<𝑥≤−5,5,−5≤𝑥<−3,−5,−3≤𝑥<2,3,2<𝑥≤4

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