Worksheet: Piecewise Functions

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

Q1:

Determine ๐‘“(0).

Q2:

In the following graph, what is ๐‘“(โˆ’4)?

Q3:

Determine ๐‘“(0) using the graph below.

Q4:

Determine ๐‘“(โˆ’3).

Q5:

Find the missing table values for ๐‘”(๐‘ฅ)=๏ณ2๐‘ฅ<โˆ’2,3โˆ’2โ‰ค๐‘ฅ<3,2๐‘ฅโ‰ฅ3.๏—๏—๏—ififif

๐‘ฅโˆ’303
๐‘”(๐‘ฅ)
  • A18,1,8
  • B8,0,8
  • C18,0,18
  • D8,1,18

Q6:

Consider the function ๐‘“(๐‘ฅ)=๏ฒ๐‘ฅ+4๐‘ฅ>4,2๐‘ฅโˆ’1โ‰ค๐‘ฅโ‰ค4,โˆ’3๐‘ฅ<โˆ’1.ififif Find ๐‘“[๐‘“(2)].

Q7:

Given that the function ๐‘“(๐‘ฅ)=๏ด6๐‘ฅโˆ’2๐‘ฅ<โˆ’6,โˆ’9๐‘ฅโˆ’1โˆ’6โ‰ค๐‘ฅโ‰ค8,โˆ’5๐‘ฅ+4๐‘ฅ>8,ififif๏Šจ๏Šฉ find the value of ๐‘“(4).

Q8:

Given that the function ๐‘“๐‘“(๐‘ฅ)=๏ณ4๐‘ฅ+1,0000โ‰ค๐‘ฅโ‰ค4,000,8๐‘ฅ+4,6004,000<๐‘ฅโ‰ค30,000,8๐‘ฅ+3,40030,000<๐‘ฅโ‰ค90,000,:ififif represents the price of electrical appliances in LE, where ๐‘ฅ is the number of appliances, find ๐‘“(52,000).

Q9:

Complete the table with the missing values of ๐‘“(๐‘ฅ) given ๐‘“(๐‘ฅ)=๏ณโˆ’3๐‘ฅ<โˆ’7,|๐‘ฅ+4|โˆ’7โ‰ค๐‘ฅโ‰คโˆ’2,2๐‘ฅ๐‘ฅ>โˆ’2.ififif

๐‘ฅโˆ’8โˆ’7โˆ’5โˆ’2โˆ’1
๐‘“(๐‘ฅ)
  • Aโˆ’3,โˆ’3,โˆ’1,2,โˆ’2
  • Bโˆ’3,3,1,2,โˆ’2
  • C3,3,1,โˆ’2,โˆ’2
  • D3,โˆ’3,โˆ’1,โˆ’2,2

Q10:

Determine ๐‘“(1).

  • A1
  • B5
  • Cundefined

Q11:

Determine ๐‘“(2).

  • A0
  • B2
  • Cundefined
  • Dโˆ’2

Q12:

Determine ๐‘“(โˆ’2).

Q13:

From the following graph, determine ๐‘“(2).

  • Aโˆ’1
  • B0
  • Cโˆ’3
  • Dundefined

Q14:

Find ๐‘“(5).

  • Aโˆ’2
  • Bโˆ’5
  • Cundefined.
  • D5

Q15:

Given that the velocity of a motorcycle is expressed by the function ๐‘ฃ(๐‘ก)=๏ณ5๐‘ก0โ‰ค๐‘กโ‰ค12,6012<๐‘ก<70,โˆ’๐‘ก+13070โ‰ค๐‘กโ‰ค130,ififif where ๐‘ก is the time in seconds, and ๐‘ฃ is the velocity in m/s, determine ๐‘ฃ(82).

Q16:

Consider the function ๐‘€(๐‘ฅ)=๏ณ๐‘ฅ,0โ‰ค๐‘ฅ<1,๐‘€(๐‘ฅ+1),๐‘ฅ<0,๐‘€(๐‘ฅโˆ’1),๐‘ฅโ‰ฅ1.

What are the values of ๐‘€(0) and ๐‘€(0.3)?

  • A๐‘€(0)=โˆ’1, ๐‘€(0.3)=โˆ’0.7
  • B๐‘€(0)=1, ๐‘€(0.3)=0.3
  • C๐‘€(0)=1, ๐‘€(0.3)=1.3
  • D๐‘€(0)=0, ๐‘€(0.3)=0.3
  • E๐‘€(0)=โˆ’1, ๐‘€(0.3)=โˆ’0.3

What are the values of ๐‘€(1.3) and ๐‘€(2.3)?

  • A๐‘€(1.3)=โˆ’0.7, ๐‘€(2.3)=โˆ’1.7
  • B๐‘€(1.3)=0.3, ๐‘€(2.3) is undefined
  • C๐‘€(1.3)=1.3, ๐‘€(2.3)=2.3
  • Dboth ๐‘€(1.3) and ๐‘€(2.3) are undefined
  • E๐‘€(1.3)=0.3, ๐‘€(2.3)=0.3

What are the values of ๐‘€(โˆ’3) and ๐‘€(678)?

  • A๐‘€(โˆ’3)=0, ๐‘€(678) is undefined
  • B๐‘€(โˆ’3) is undefined, ๐‘€(678)=0
  • Cboth ๐‘€(โˆ’3) and ๐‘€(678) are undefined
  • D๐‘€(โˆ’3)=0, ๐‘€(678)=0
  • E๐‘€(โˆ’3)=โˆ’3, ๐‘€(678)=678

What is the domain of the function ๐‘€?

  • A[โˆ’1,2)
  • B[0,1)
  • Cโ„
  • Dโ„โงตโ„ค
  • E[0,1]

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