Worksheet: Piecewise Functions

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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‘ฅ โˆ’ 3 0 3
๐‘” ( ๐‘ฅ )
  • A 1 8 , 1 , 8
  • B 8 , 0 , 8
  • C 1 8 , 0 , 1 8
  • D 8 , 1 , 1 8

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‘ฅ โˆ’ 8 โˆ’ 7 โˆ’ 5 โˆ’ 2 โˆ’ 1
๐‘“ ( ๐‘ฅ )
  • A โˆ’ 3 , โˆ’ 3 , โˆ’ 1 , 2 , โˆ’ 2
  • B โˆ’ 3 , 3 , 1 , 2 , โˆ’ 2
  • C 3 , 3 , 1 , โˆ’ 2 , โˆ’ 2
  • D 3 , โˆ’ 3 , โˆ’ 1 , โˆ’ 2 , 2

Q10:

Determine ๐‘“(1).

  • A1
  • B5
  • Cundefined

Q11:

Determine ๐‘“(2).

  • A0
  • B2
  • Cundefined
  • D โˆ’ 2

Q12:

Determine ๐‘“(โˆ’2).

Q13:

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

  • A โˆ’ 1
  • B0
  • C โˆ’ 3
  • Dundefined

Q14:

Find ๐‘“(5).

  • A โˆ’ 2
  • B โˆ’ 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)?

  • A ๐‘€ ( 0 ) = โˆ’ 1 , ๐‘€ ( 0 . 3 ) = โˆ’ 0 . 7
  • B ๐‘€ ( 0 ) = 1 , ๐‘€ ( 0 . 3 ) = 0 . 3
  • C ๐‘€ ( 0 ) = 1 , ๐‘€ ( 0 . 3 ) = 1 . 3
  • D ๐‘€ ( 0 ) = 0 , ๐‘€ ( 0 . 3 ) = 0 . 3
  • E ๐‘€ ( 0 ) = โˆ’ 1 , ๐‘€ ( 0 . 3 ) = โˆ’ 0 . 3

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

  • A ๐‘€ ( 1 . 3 ) = โˆ’ 0 . 7 , ๐‘€ ( 2 . 3 ) = โˆ’ 1 . 7
  • B ๐‘€ ( 1 . 3 ) = 0 . 3 , ๐‘€ ( 2 . 3 ) is undefined
  • C ๐‘€ ( 1 . 3 ) = 1 . 3 , ๐‘€ ( 2 . 3 ) = 2 . 3
  • Dboth ๐‘€(1.3) and ๐‘€(2.3) are undefined
  • E ๐‘€ ( 1 . 3 ) = 0 . 3 , ๐‘€ ( 2 . 3 ) = 0 . 3

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

  • A ๐‘€ ( โˆ’ 3 ) = 0 , ๐‘€ ( 6 7 8 ) is undefined
  • B ๐‘€ ( โˆ’ 3 ) is undefined, ๐‘€(678)=0
  • Cboth ๐‘€(โˆ’3) and ๐‘€(678) are undefined
  • D ๐‘€ ( โˆ’ 3 ) = 0 , ๐‘€ ( 6 7 8 ) = 0
  • E ๐‘€ ( โˆ’ 3 ) = โˆ’ 3 , ๐‘€ ( 6 7 8 ) = 6 7 8

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

  • A [ โˆ’ 1 , 2 )
  • B [ 0 , 1 )
  • C โ„
  • D โ„ โงต โ„ค
  • E [ 0 , 1 ]

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