Lesson Worksheet: Piecewise Functions Mathematics

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:

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).

Q6:

Given that the function ๐‘“๐‘“(๐‘ฅ)=๏ฒ4๐‘ฅ+1,000,0โ‰ค๐‘ฅโ‰ค4,000,8๐‘ฅ+4,600,4,000<๐‘ฅโ‰ค30,000,8๐‘ฅ+3,400,30,000<๐‘ฅโ‰ค90,000,: represents the price of electrical appliances in LE, where ๐‘ฅ is the number of appliances, find ๐‘“(52,000).

Q7:

Determine ๐‘“(1).

  • A1
  • B5
  • Cundefined

Q8:

Determine ๐‘“(2).

  • A0
  • B2
  • Cundefined
  • Dโˆ’2

Q9:

Determine ๐‘“(โˆ’2).

Q10:

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

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

Q11:

Find ๐‘“(5).

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

Q12:

Given that the velocity of a motorcycle is expressed by the function ๐‘ฃ(๐‘ก)=๏ฒ5๐‘ก,0โ‰ค๐‘กโ‰ค12,60,12<๐‘ก<70,โˆ’๐‘ก+130,70โ‰ค๐‘กโ‰ค130, where ๐‘ก is the time in seconds, and ๐‘ฃ is the velocity in m/s, determine ๐‘ฃ(82).

Q13:

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]

Q14:

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

Q15:

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)].

Q16:

Complete the table with the missing values of ๐‘“(๐‘ฅ) given ๐‘“(๐‘ฅ)=๏ฒโˆ’3,๐‘ฅ<โˆ’7,|๐‘ฅ+4|,โˆ’7โ‰ค๐‘ฅโ‰คโˆ’2,2๐‘ฅ,๐‘ฅ>โˆ’2.

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

Q17:

The function ๐‘“(๐‘ฅ)=๏ฒ20๐‘ฅ+4,000,1โ‰ค๐‘ฅโ‰ค4,30๐‘ฅ+5,000,4<๐‘ฅโ‰ค10,60๐‘ฅ+7,000,10<๐‘ฅ<15 models the sales, in dollars, of a product in a store after ๐‘ฅ years of business.

Determine the sales after 2 years of business.

If the sales in a specific year were $4,060, what were the sales 2 years before?

Q18:

The salary of an employee is $1,500 per month. He works between 140 and 150 hours inclusive, and he gets $16 for every extra hour he works past the 150 hours.

Let ๐‘ฅ be the number of hours he works per month and ๐‘“(๐‘ฅ) be the total salary he gains per month.

Which of the following is the piecewise representation of ๐‘“(๐‘ฅ)?

  • A๐‘“(๐‘ฅ)=๏ญ1,500,140โ‰ค๐‘ฅโ‰ค150,1,516๐‘ฅ,๐‘ฅ>150
  • B๐‘“(๐‘ฅ)=๏ญ1,500,140โ‰ค๐‘ฅโ‰ค150,1,500+16(๐‘ฅโˆ’150),๐‘ฅ>150
  • C๐‘“(๐‘ฅ)=๏ญ1,500,140โ‰ค๐‘ฅ<150,1,516๐‘ฅ,๐‘ฅโ‰ฅ150
  • D๐‘“(๐‘ฅ)=๏ญ1,500,140โ‰ค๐‘ฅโ‰ค150,16๐‘ฅ,๐‘ฅ>150
  • E๐‘“(๐‘ฅ)=๏ญ1,500,140โ‰ค๐‘ฅโ‰ค150,1,500+16๐‘ฅ,๐‘ฅ>150

Find the total salary of two months if the employee worked an extra 3 hours in the first month and an extra 2 hours in the second month.

Q19:

Find the value of ๐‘Ž such that ๐‘“(๐‘ฅ)=๏ญ3๐‘ฅ+2๐‘Ž,๐‘ฅโ‰ค1,๐‘ฅ+4,๐‘ฅ>1 and ๐‘“(โˆ’4)=2.

Q20:

A company specialized in manufacturing clothes uses the function ๐ถ(๐‘ฅ)=๏ญ12,000,0<๐‘ฅ<5,12,000+2,000(๐‘ฅโˆ’4),๐‘ฅโ‰ฅ5 to determine the cost, ๐ถ(๐‘ฅ), in dollars, of the number of units, ๐‘ฅ, of used fabric.

Find the cost of using 6 units of fabric.

Find the maximum number of units needed to ensure that the cost will not exceed $34,000.

Q21:

Does the graph of the function

๐‘“(๐‘ฅ)=๏ญโˆ’5๐‘ฅ+1,0<๐‘ฅโ‰ค24,3๐‘ฅ+4,๐‘ฅ>24

include the point (20,โˆ’99)?

  • ANo
  • BYes

Q22:

Consider the function ๐‘“(๐‘ฅ)=๏ฒโˆ’3๐‘ฅ+40โ‰ค๐‘ฅ<6,2๐‘ฅโˆ’16โ‰ค๐‘ฅ<12,โˆ’6๐‘ฅ+9๐‘ฅโ‰ฅ12.

Find the value of ๐‘“(6).

Find the value of ๐‘“(12).

Find the value of ๐‘“(4).

Q23:

Given the function ๐‘“(๐‘ฅ)=๏ญ3๐‘ฅโˆ’1,โˆ’1โ‰ค๐‘ฅ<10,2๐‘ฅ+11,๐‘ฅโ‰ฅ10, find the value of ๐‘Ž such that ๐‘“(๐‘Ž)=2.

Q24:

Given that ๐‘“(๐‘ฅ)=๏ญ๐‘ฅ+12,0โ‰ค๐‘ฅ<๐‘Ž,๐‘ฅ+34,๐‘Žโ‰ค๐‘ฅโ‰ค6,๏Šจ find the value of ๐‘Ž, where ๐‘Žโˆˆโ„ค, ๐‘“(4)=16, and ๐‘“(5)=59.

Q25:

The function ๐‘“(๐‘ฅ) can be represented by the graph shown.

Which of the following is the piecewise representation of ๐‘“(๐‘ฅ)?

  • A๐‘“(๐‘ฅ)=๏ฒ๐‘ฅโˆ’1โˆ’2โ‰ค๐‘ฅ<4254<๐‘ฅโ‰ค102๐‘ฅ+8๐‘ฅ>10๏Šจ
  • B๐‘“(๐‘ฅ)=๏ฒ๐‘ฅ+1โˆ’2โ‰ค๐‘ฅ<4254<๐‘ฅ<102๐‘ฅ+8๐‘ฅโ‰ฅ10๏Šจ
  • C๐‘“(๐‘ฅ)=๏ฒ๐‘ฅ+1โˆ’2โ‰ค๐‘ฅ<4254<๐‘ฅโ‰ค102๐‘ฅ+8๐‘ฅ>10๏Šจ
  • D๐‘“(๐‘ฅ)=๏ฒ๐‘ฅโˆ’1โˆ’2โ‰ค๐‘ฅ<4254โ‰ค๐‘ฅโ‰ค102๐‘ฅ+8๐‘ฅ>10๏Šจ
  • E๐‘“(๐‘ฅ)=๏ฒ๐‘ฅโˆ’1โˆ’2โ‰ค๐‘ฅ<425๐‘ฅ4<๐‘ฅโ‰ค102๐‘ฅ+8๐‘ฅ>10๏Šจ

Find the value of ๐‘“(3).

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