Worksheet: Evaluating Piecewise Functions

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In this worksheet, we will practice finding the value of piecewise functions from the graphs of the functions.

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 ) = ๏ณ 2 ๐‘ฅ < โˆ’ 2 , 3 โˆ’ 2 โ‰ค ๐‘ฅ < 3 , 2 ๐‘ฅ โ‰ฅ 3 . ๏— ๏— ๏— i f i f i f

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

Q6:

Consider the function Find ๐‘“ [ ๐‘“ ( 2 ) ] .

Q7:

Given that the function ๐‘“ ( ๐‘ฅ ) = ๏ด 6 ๐‘ฅ โˆ’ 2 ๐‘ฅ < โˆ’ 6 , โˆ’ 9 ๐‘ฅ โˆ’ 1 โˆ’ 6 โ‰ค ๐‘ฅ โ‰ค 8 , โˆ’ 5 ๐‘ฅ + 4 ๐‘ฅ > 8 , i f i f i f ๏Šจ ๏Šฉ find the value of ๐‘“ ( 4 ) .

Q8:

Given that the function ๐‘“ ๐‘“ ( ๐‘ฅ ) = ๏ณ 4 ๐‘ฅ + 1 , 0 0 0 0 โ‰ค ๐‘ฅ โ‰ค 4 , 0 0 0 , 8 ๐‘ฅ + 4 , 6 0 0 4 , 0 0 0 < ๐‘ฅ โ‰ค 3 0 , 0 0 0 , 8 ๐‘ฅ + 3 , 4 0 0 3 0 , 0 0 0 < ๐‘ฅ โ‰ค 9 0 , 0 0 0 , : i f i f i f represents the price of electrical appliances in LE, where ๐‘ฅ is the number of appliances, find ๐‘“ ( 5 2 , 0 0 0 ) .

Q9:

Complete the table with the missing values of ๐‘“ ( ๐‘ฅ ) given ๐‘“ ( ๐‘ฅ ) = ๏ณ โˆ’ 3 ๐‘ฅ < โˆ’ 7 , | ๐‘ฅ + 4 | โˆ’ 7 โ‰ค ๐‘ฅ โ‰ค โˆ’ 2 , 2 ๐‘ฅ ๐‘ฅ > โˆ’ 2 . i f i f i f

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

Q10:

Determine ๐‘“ ( 1 ) .

  • A5
  • B1
  • Cundefined

Q11:

Determine ๐‘“ ( 2 ) .

  • A2
  • B โˆ’ 2
  • C0
  • Dundefined

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’ 5
  • B5
  • C โˆ’ 2
  • Dundefined.

Q15:

Given that the velocity of a motorcycle is expressed by the function ๐‘ฃ ( ๐‘ก ) = ๏ณ 5 ๐‘ก 0 โ‰ค ๐‘ก โ‰ค 1 2 , 6 0 1 2 < ๐‘ก < 7 0 , โˆ’ ๐‘ก + 1 3 0 7 0 โ‰ค ๐‘ก โ‰ค 1 3 0 , i f i f i f where ๐‘ก is the time in seconds, and ๐‘ฃ is the velocity in m/s, determine ๐‘ฃ ( 8 2 ) .

Q16:

Consider the function ๐‘€ ( ๐‘ฅ ) = ๏ณ ๐‘ฅ , 0 โ‰ค ๐‘ฅ < 1 , ๐‘€ ( ๐‘ฅ + 1 ) , ๐‘ฅ < 0 , ๐‘€ ( ๐‘ฅ โˆ’ 1 ) , ๐‘ฅ โ‰ฅ 1 .

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

What are the values of ๐‘€ ( 1 . 3 ) and ๐‘€ ( 2 . 3 ) ?

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

What are the values of ๐‘€ ( โˆ’ 3 ) and ๐‘€ ( 6 7 8 ) ?

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

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

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

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