Worksheet: Evaluating a Function at a Given Value

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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 ∶ ℝ → ℝ , 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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