Lesson Worksheet: Piecewise Functions Mathematics

In this worksheet, we will practice identifying, writing, and evaluating a piecewise function.

Q1:

Determine 𝑓(0).

Q2:

Determine 𝑓(0) using the graph below.

Q3:

Given that the function 𝑓(𝑥)=6𝑥2𝑥<6,9𝑥16𝑥8,5𝑥+4𝑥>8,ififif find the value of 𝑓(4).

Q4:

Given that the velocity of a motorcycle is expressed by the function 𝑣(𝑡)=5𝑡,0𝑡12,60,12<𝑡<70,𝑡+130,70𝑡130, where 𝑡 is the time in seconds, and 𝑣 is the velocity in m/s, determine 𝑣(82).

Q5:

Given the function 𝑓(𝑥)=3𝑥1,1𝑥<10,2𝑥+11,𝑥10, find the value of 𝑎 such that 𝑓(𝑎)=2.

Q6:

Determine 𝑓(1).

  • A1
  • B5
  • Cundefined

Q7:

Determine 𝑓(2).

Q8:

Find the missing table values for 𝑔(𝑥)=2𝑥<2,32𝑥<3,2𝑥3.ififif

𝑥303
𝑔(𝑥)
  • A18,1,8
  • B8,0,8
  • C18,0,18
  • D8,1,18

Q9:

The function 𝑓(𝑥) can be represented by the graph shown.

Which of the following is the piecewise representation of 𝑓(𝑥)?

  • A𝑓(𝑥)=𝑥12𝑥<4254<𝑥102𝑥+8𝑥>10
  • B𝑓(𝑥)=𝑥+12𝑥<4254<𝑥<102𝑥+8𝑥10
  • C𝑓(𝑥)=𝑥+12𝑥<4254<𝑥102𝑥+8𝑥>10
  • D𝑓(𝑥)=𝑥12𝑥<4254𝑥102𝑥+8𝑥>10
  • E𝑓(𝑥)=𝑥12𝑥<425𝑥4<𝑥102𝑥+8𝑥>10

Find the value of 𝑓(3).

Q10:

Consider the function 𝑓(𝑥)=𝑥+4𝑥>4,2𝑥1𝑥4,3𝑥<1.ififif Find 𝑓[𝑓(2)].

This lesson includes 24 additional questions and 248 additional question variations for subscribers.

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