Lesson Worksheet: Piecewise Functions Mathematics

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

Q1:

Determine 𝑓(0).

Q2:

In the following graph, what is 𝑓(4)?

Q3:

Determine 𝑓(0) using the graph below.

Q4:

Determine 𝑓(3).

Q5:

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

Q6:

Given that the function 𝑓𝑓(𝑥)=4𝑥+1,000,0𝑥4,000,8𝑥+4,600,4,000<𝑥30,000,8𝑥+3,400,30,000<𝑥90,000,: represents the price of electrical appliances in LE, where 𝑥 is the number of appliances, find 𝑓(52,000).

Q7:

Determine 𝑓(1).

  • A1
  • B5
  • Cundefined

Q8:

Determine 𝑓(2).

  • A0
  • B2
  • Cundefined
  • D2

Q9:

Determine 𝑓(2).

Q10:

From the following graph, determine 𝑓(2).

  • A1
  • B0
  • C3
  • Dundefined

Q11:

Find 𝑓(5).

  • A2
  • B5
  • Cundefined.
  • D5

Q12:

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).

Q13:

Consider the function 𝑀(𝑥)=𝑥,0𝑥<1,𝑀(𝑥+1),𝑥<0,𝑀(𝑥1),𝑥1.

What are the values of 𝑀(0) and 𝑀(0.3)?

  • A𝑀(0)=1, 𝑀(0.3)=0.7
  • B𝑀(0)=1, 𝑀(0.3)=0.3
  • C𝑀(0)=1, 𝑀(0.3)=1.3
  • D𝑀(0)=0, 𝑀(0.3)=0.3
  • E𝑀(0)=1, 𝑀(0.3)=0.3

What are the values of 𝑀(1.3) and 𝑀(2.3)?

  • A𝑀(1.3)=0.7, 𝑀(2.3)=1.7
  • B𝑀(1.3)=0.3, 𝑀(2.3) is undefined
  • C𝑀(1.3)=1.3, 𝑀(2.3)=2.3
  • Dboth 𝑀(1.3) and 𝑀(2.3) are undefined
  • E𝑀(1.3)=0.3, 𝑀(2.3)=0.3

What are the values of 𝑀(3) and 𝑀(678)?

  • A𝑀(3)=0, 𝑀(678) is undefined
  • B𝑀(3) is undefined, 𝑀(678)=0
  • Cboth 𝑀(3) and 𝑀(678) are undefined
  • D𝑀(3)=0, 𝑀(678)=0
  • E𝑀(3)=3, 𝑀(678)=678

What is the domain of the function 𝑀?

  • A[1,2)
  • B[0,1)
  • C
  • D
  • E[0,1]

Q14:

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

Q15:

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

Q16:

Complete the table with the missing values of 𝑓(𝑥) given 𝑓(𝑥)=3,𝑥<7,|𝑥+4|,7𝑥2,2𝑥,𝑥>2.

𝑥87521
𝑓(𝑥)
  • A3, 3, 1, 2, 2
  • B3, 3, 1, 2, 2
  • C3, 3, 1, 2, 2
  • D3, 3, 1, 2, 2

Q17:

The function 𝑓(𝑥)=20𝑥+4,000,1𝑥4,30𝑥+5,000,4<𝑥10,60𝑥+7,000,10<𝑥<15 models the sales, in dollars, of a product in a store after 𝑥 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 𝑥 be the number of hours he works per month and 𝑓(𝑥) be the total salary he gains per month.

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

  • A𝑓(𝑥)=1,500,140𝑥150,1,516𝑥,𝑥>150
  • B𝑓(𝑥)=1,500,140𝑥150,1,500+16(𝑥150),𝑥>150
  • C𝑓(𝑥)=1,500,140𝑥<150,1,516𝑥,𝑥150
  • D𝑓(𝑥)=1,500,140𝑥150,16𝑥,𝑥>150
  • E𝑓(𝑥)=1,500,140𝑥150,1,500+16𝑥,𝑥>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 𝑎 such that 𝑓(𝑥)=3𝑥+2𝑎,𝑥1,𝑥+4,𝑥>1 and 𝑓(4)=2.

Q20:

A company specialized in manufacturing clothes uses the function 𝐶(𝑥)=12,000,0<𝑥<5,12,000+2,000(𝑥4),𝑥5 to determine the cost, 𝐶(𝑥), in dollars, of the number of units, 𝑥, 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

𝑓(𝑥)=5𝑥+1,0<𝑥24,3𝑥+4,𝑥>24

include the point (20,99)?

  • ANo
  • BYes

Q22:

Consider the function 𝑓(𝑥)=3𝑥+40𝑥<6,2𝑥16𝑥<12,6𝑥+9𝑥12.

Find the value of 𝑓(6).

Find the value of 𝑓(12).

Find the value of 𝑓(4).

Q23:

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

Q24:

Given that 𝑓(𝑥)=𝑥+12,0𝑥<𝑎,𝑥+34,𝑎𝑥6, find the value of 𝑎, where 𝑎, 𝑓(4)=16, and 𝑓(5)=59.

Q25:

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).

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