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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:

Find 𝑦 , given the point ( βˆ’ 2 , 𝑦 ) lies on the function 𝑓 ( π‘₯ ) = βˆ’ 6 π‘₯ βˆ’ 1 0 π‘₯ + 8 2 .

Q2:

Find 𝑦 , given the point ( βˆ’ 4 , 𝑦 ) lies on the function 𝑓 ( π‘₯ ) = βˆ’ 8 π‘₯ + 5 2 .

Q3:

Given that the function 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯ + 1 0 π‘₯ βˆ’ 2 2 , where 𝑓 ∢ ℝ β†’ ℝ , determine 𝑓 ( 3 ) .

Q4:

Which of the following set of coordinates lies on 𝑓 ( π‘₯ ) = βˆ’ 1 9 π‘₯ βˆ’ 1 6 .

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

Q5:

Which of the following set of coordinates lies on 𝑓 ( π‘₯ ) = 1 3 π‘₯ βˆ’ 1 3 .

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

Q6:

Find the value of 4 𝑓 ο€» √ 3  βˆ’ 4 𝑔 ο€» √ 3  given the function 𝑓 ( π‘₯ ) = π‘₯ + 7 π‘₯ 2 and the function 𝑔 ( π‘₯ ) = 7 π‘₯ βˆ’ 4 .

Q7:

Using the function 𝑦 = π‘₯ + 3 2 , calculate the corresponding output for an input of 2.

Q8:

Complete the given table of values for the function 𝑦 = 3 π‘₯ βˆ’ 2 π‘₯ 2 .

π‘₯ βˆ’ 2 βˆ’ 1 0 1 2
𝑦
  • A βˆ’ 1 6 , βˆ’ 5 , 0 , 1 , 8
  • B βˆ’ 8 , βˆ’ 1 , 0 , 1 , 8
  • C βˆ’ 8 , βˆ’ 1 , 1 , 5 , 1 6
  • D 1 6 , 5 , 0 , 1 , 8
  • E βˆ’ 1 6 , βˆ’ 5 , 1 , 5 , 1 6

Q9:

Complete the given table of values for the function 𝑦 = 1 5 βˆ’ 7 π‘₯ + 8 π‘₯ 2 .

π‘₯ βˆ’ 2 βˆ’ 1 0 1 2
𝑦

Q10:

Given that the point ( 3 , 𝑦 ) lies on the graph of 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 π‘₯ + 4 2 , find 𝑦 .

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

Q11:

Find 𝑓 ( 5 ) + 𝑓 ( βˆ’ 8 ) given the function 𝑓 ( π‘₯ ) = βˆ’ 1 1 .

Q12:

Find 𝑓 ( 3 ) + 𝑓 ( βˆ’ 6 ) given the function 𝑓 ( π‘₯ ) = βˆ’ 1 0 .

Q13:

If 𝑓 ( π‘₯ ) = 7 π‘₯ βˆ’ 4 π‘₯ βˆ’ 5 2 , find 𝑓 ο€» 4 + √ 6  βˆ’ 𝑓 ο€» 4 βˆ’ √ 6  .

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

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