Worksheet: Evaluating a Function at a Given Value

In this worksheet, we will practice calculating the value (or output) of a function given a specified input.

Q1:

Which of the following set of coordinates lies on 𝑓 ( 𝑥 ) = 1 9 𝑥 1 6 ?

  • A ( 1 0 , 1 6 )
  • B ( 2 0 6 , 1 0 )
  • C ( 2 0 6 , 1 6 )
  • D ( 1 0 , 2 0 6 )

Q2:

Find 𝑦 , given the point ( 2 , 𝑦 ) lies on the function 𝑓 ( 𝑥 ) = 6 𝑥 1 0 𝑥 + 8 .

Q3:

Several fish were accidentally released into a lake. After 𝑛 weeks, the number of fish is estimated to be 𝑓 ( 𝑛 ) = 5 9 ( 1 . 1 ) 𝑛 . Determine the likely number of fish in the lake after 5 weeks. Give your answer to the nearest whole number.

  • A35
  • B325
  • C266
  • D95

Q4:

Find 𝑓 ( 5 ) + 𝑓 ( 8 ) given the function 𝑓 ( 𝑥 ) = 1 1 .

Q5:

Given that the function 𝑓 ( 𝑥 ) = 2 𝑥 + 1 0 𝑥 2 2 , where 𝑓 , determine 𝑓 ( 3 ) .

Q6:

Using the function 𝑦 = 𝑥 + 3 2 , calculate the corresponding output for an input of 2.

Q7:

Find the value of 4 𝑓 3 4 𝑔 3 given the function 𝑓 ( 𝑥 ) = 𝑥 + 7 𝑥 2 and the function 𝑔 ( 𝑥 ) = 7 𝑥 4 .

Q8:

Complete the given table of values for the function 𝑦 = 3 𝑥 2 𝑥 .

𝑥 2 1 0 1 2
𝑦
  • A 1 6 , 5 , 0 , 1 , 8
  • B 8 , 1 , 0 , 1 , 8
  • C 8 , 1 , 1 , 5 , 1 6
  • D 1 6 , 5 , 0 , 1 , 8
  • E 1 6 , 5 , 1 , 5 , 1 6

Q9:

Complete the given table of values for the function 𝑦 = 1 5 7 𝑥 + 8 𝑥 2 .

𝑥 2 1 0 1 2
𝑦

Q10:

Given that the point ( 3 , 𝑦 ) lies on the graph of 𝑓 ( 𝑥 ) = 𝑥 3 𝑥 + 4 2 , find 𝑦 .

  • A 𝑦 = 2
  • B 𝑦 = 1
  • C 𝑦 = 1 0
  • D 𝑦 = 4
  • E 𝑦 = 4

Q11:

If 𝑓 ( 𝑥 ) = 7 𝑥 4 𝑥 5 2 , find 𝑓 4 + 6 𝑓 4 6 .

  • A 1 0 4 6 + 2 6 6
  • B266
  • C 1 0 4 6 + 2 6 6
  • D 1 0 4 6
  • E 1 0 4 6

Q12:

Find 𝑦 , given the point ( 4 , 𝑦 ) lies on the function 𝑓 ( 𝑥 ) = 8 𝑥 + 5 .

Q13:

Which of the following set of coordinates lies on 𝑓 ( 𝑥 ) = 1 3 𝑥 1 3 ?

  • A ( 6 , 1 3 )
  • B ( 6 5 , 6 )
  • C ( 6 5 , 1 3 )
  • D ( 6 , 6 5 )

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