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: 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

Q6:

State the domain and range of the function 𝑓(𝑥)=3,5<𝑥1,4,1<𝑥<4,6,4𝑥<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)=8,11𝑥<8,4,8<𝑥<2,2,2𝑥<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,𝑎𝑥<1,𝑏,1𝑥<3,4,3𝑥<7.

If its domain is 5𝑥<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<𝑥5,5,5<𝑥<3,5,3<𝑥<2,3,2<𝑥4
  • B𝑓(𝑥)=9,10<𝑥5,5,5<𝑥<3,5,3𝑥<2,3,2<𝑥<4
  • C𝑓(𝑥)=9,10<𝑥5,5,5<𝑥<3,5,3𝑥<2,3,2<𝑥4
  • D𝑓(𝑥)=9,10<𝑥<5,5,5<𝑥<3,5,3𝑥<2,3,2<𝑥4
  • E𝑓(𝑥)=9,10<𝑥5,5,5𝑥<3,5,3𝑥<2,3,2<𝑥4

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