Worksheet: Evaluating Functions

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In this worksheet, we will practice calculating the value (or output) of a function using its equation or its graph.

Q1:

Which of the following set of coordinates lies on 𝑓(𝑥)=−19𝑥−16?

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

Q2:

Find 𝑦, given the point (−2,𝑦) lies on the function 𝑓(𝑥)=−6𝑥−10𝑥+8.

Q3:

Several fish were accidentally released into a lake. After 𝑛 weeks, the number of fish is estimated to be 𝑓(𝑛)=59(1.1). Determine the likely number of fish in the lake after 5 weeks. Give your answer to the nearest whole number.

  • A325
  • B35
  • C95
  • D266

Q4:

Find 𝑓(5)+𝑓(−8) given the function 𝑓(𝑥)=−11.

Q5:

Given that the function 𝑓(𝑥)=−2𝑥+10𝑥−2, where 𝑓∶ℝ→ℝ, determine 𝑓(3).

Q6:

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

Q7:

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

Q8:

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

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

Q9:

Complete the given table of values for the function 𝑦=15−7𝑥+8𝑥.

𝑥 − 2 − 1 0 1 2
𝑦
  • A − 2 9 , 0 , 1 5 , 1 6 , 3
  • B 2 7 , 1 4 , 8 , 1 4 , − 3
  • C 5 9 , 3 0 , 1 5 , 1 6 , 3
  • D − 2 9 , 0 , 8 , 1 4 , − 3
  • E 2 7 , 1 4 , 1 5 , 1 6 , 3

Q10:

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

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

Q11:

If 𝑓(𝑥)=7𝑥−4𝑥−5, find 𝑓4+√6−𝑓4−√6.

  • A − 1 0 4 √ 6 + 2 6 6
  • B 1 0 4 √ 6 + 2 6 6
  • C 1 0 4 √ 6
  • D − 1 0 4 √ 6
  • E266

Q12:

Find 𝑦, given the point (−3,𝑦) lies on the function 𝑓(𝑥)=−7𝑥+𝑥−8.

Q13:

Which of the following set of coordinates lies on 𝑓(𝑥)=13𝑥−13?

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

Q14:

Which of the following is NOT a point on the curve 𝑓(𝑥)=𝑥+3𝑥−5?

  • A ( − 3 , − 5 )
  • B ( 1 , − 2 )
  • C ( 1 , − 1 )
  • D ( 0 , − 5 )
  • E ( − 2 , − 1 )

Q15:

A function 𝑓 maps the positive integers onto a set 𝑆. For example, if 𝑓(𝑥)=2𝑥 then 𝑆 would be the set of even integers {2,4,6,8,…}

What sequence is produced by inputing the positive integers into 𝑔(𝑥)=2𝑥−1.

  • A { 1 , 2 , 3 , 4 , … }
  • B { 1 , 4 , 6 , 8 , … }
  • C { 2 , 4 , 6 , 8 , … }
  • D { 2 , 5 , 8 , 9 , … }
  • E { 1 , 3 , 5 , 7 , … }

Which of the following describes 𝑔(10)=19?.

  • A19 is the ninth positive odd integer.
  • B19 is the tenth positive odd integer.
  • C19 is the eleventh positive odd integer.
  • D19 is the eighth positive odd integer.
  • E19 is the sixth positive odd integer.

Write the first 5 terms of the sequence given by ℎ(𝑥)=(−1)+1.

  • A { 0 , 1 , 0 , 1 , 0 }
  • B { 0 , 2 , 0 , 2 , 0 }
  • C { 2 , 0 , 2 , 0 , 2 }
  • D { 1 , 0 , 1 , 0 , 1 }
  • E { 0 , − 2 , 0 , − 2 , 0 }

Which of the following functions produces the sequence {1,0,1,0,…}?

  • A 𝑓 ( 𝑥 ) = 1 − ( − 1 ) 2
  • B 𝑓 ( 𝑥 ) = 2 + ( − 1 ) 2
  • C 𝑓 ( 𝑥 ) = 1 2 − ( − 1 )
  • D 𝑓 ( 𝑥 ) = 1 + ( − 1 )
  • E 𝑓 ( 𝑥 ) = 2 − ( − 1 )

Q16:

Given a function 𝑓, the meaning of 𝑓(𝑎−1) is “the output when the input is 1 less than 𝑎.” Interpret the following.

𝑓 ( 𝑏 + 3 )

  • A3 more than the output when the input is 𝑏
  • Bthe output when the input is 3 more than 𝑏
  • C 𝑏 + 3 times the output
  • D 𝑏 + 3 times the input
  • Ethe input when the ouput is 3 more than 𝑏

𝑓 ( 𝑠 ) − 3

  • A3 less than the output when the input is 𝑠
  • B3 more than the input when the output is 𝑠
  • C3 less than the input when the output is 𝑠
  • DThe output is 3 when the input is 𝑠.
  • E3 more than the output when the input is 𝑠

𝑓 ( 3 − 𝑥 )

  • Athe output when the input is 𝑥 less than 3
  • Bthe output when the input is 𝑥 more than 3
  • Cthe input when the ouput is 𝑥 less than 3
  • Dthe input when the ouput is 𝑥 more than 3

𝑓 ( 𝑏 ) − 𝑓 ( 𝑎 )

  • Athe change in input when the output changes from 𝑏 to 𝑎
  • Bthe change in output when the input changes from 𝑎 to 𝑏
  • Cthe change in output when the input changes from 𝑏 to 𝑎
  • Dthe change in input when the output changes from 𝑎 to 𝑏

𝑓 ( 3 𝑡 )

  • Athe output when the input is 𝑡
  • B3 more than the output when the input is 𝑡
  • Cthe output when the input is 3 times 𝑡
  • Dthe input when the output is 3 times 𝑡
  • Ethe output when the input is 3

𝑓 ( 𝑎 )

  • Athe result of raising the input at output 𝑎 to the 𝑏th power
  • Bthe result of raising the output at input 𝑏 to the 𝑎th power
  • Cthe result of raising the input at output 𝑏 to the 𝑎th power
  • Dthe result of raising the output at input 𝑎 to the 𝑏th power

Q17:

The function 𝐷(𝑡) records Benjamin’s distance in kilometers from his home 𝑡 minutes after he begins the measurements. Write the given statements in words.

𝐷 ( 0 ) = 0 . 5

  • ABenjamin reaches his home after 0.5 km.
  • BBenjamin starts measurement when he is more than 0.5 km from home.
  • CBenjamin starts measurements when he is 0.5 km from home.
  • DBenjamin starts measurements when he is at home.

𝐷 ( 6 0 ) = 0

  • ABenjamin starts measurements when he is 60 minutes from home.
  • BBenjamin starts measurements when he is 60 km from home.
  • CBenjamin is home after an hour.

𝐷 ( 2 3 ) = 𝐷 ( 3 2 )

  • ABenjamin is at different distances from home at both the 23rd and 32nd minute.
  • BBenjamin is the same time from home at both the 23rd and 32nd kilometer.
  • CBenjamin is the same distance from home at both the 23rd and 32nd minute.

𝐷 ( 1 6 ) > 𝐷 ( 1 2 )

  • ABenjamin is closer to home at 16 minutes than at 12 minutes after the start.
  • BBenjamin is closer to home at 16 km than at 12 km after the start.
  • CBenjamin is farther away from home at 16 minutes than at 12 minutes after the start.
  • DBenjamin is farther away from home at 16 km than at 12 km after the start.

𝐷 ( 𝑎 ) = 1 . 2

  • AAt time 𝑎, Benjamin is 1.2 km from home.
  • BAt time 1.2 minutes, Benjamin is 2𝑎 km from home.
  • CAt time 1.2 minutes, Benjamin is 𝑎 km from home.
  • DAt time 𝑎, Benjamin is 2.4 km from home.

𝐷 ( 1 3 ) = 𝑏

  • AAfter 𝑏 minutes, Benjamin is 26 km from home.
  • BAfter 13 minutes, Benjamin is 2𝑏 km from home.
  • CAfter 𝑏 minutes, Benjamin is 13 km from home.
  • DAfter 13 minutes, Benjamin is 𝑏 km from home.

Q18:

You put a sweet potato, that has been left on the side in the kitchen, in the oven. After 45 minutes, you take it out. Let 𝑓(𝑡) be the temperature of the potato 𝑡 minutes after you placed it in the oven. Rewrite each of these statements using function notation.

As you put the potato in the oven, the room temperature was 20.

  • A 𝑓 ( 0 ) > 2 0
  • B 𝑓 ( 0 ) = 2 0
  • C 𝑓 ( 0 ) < 2 0
  • D 𝑓 ( 2 0 ) > 0
  • E 𝑓 ( 2 0 ) = 0

The potato was hotter at 10 minutes than at 5.

  • A 𝑓 ( 5 ) < 𝑓 ( 1 0 )
  • B 𝑓 ( 5 ) = 𝑓 ( 1 0 )
  • C 𝑓 ( 5 ) > 𝑓 ( 1 0 )

The potato was at the same temperature at 40 minutes as it was when taken out.

  • A 𝑓 ( 4 0 ) < 𝑓 ( 4 5 )
  • B 𝑓 ( 4 0 ) = 𝑓 ( 4 5 )
  • C 𝑓 ( 4 0 ) > 𝑓 ( 4 5 )

Q19:

Find ℎ(2), if ℎ(𝑥)=𝑓(𝑥)𝑔(𝑥) and 𝑓(𝑥)=𝑥−𝑥+1, 𝑔(𝑥)=𝑥+1.

Q20:

The function 𝑓 is given by 𝑓(𝑥)= the greatest integer that is less than or equal to 𝑥. Which of the following is not true of this function?

  • AThe range of 𝑓 is the set of all integers.
  • B 𝑓 ( − 0 . 5 ) = − 1
  • CThe domain of 𝑓 is assumed to be the set of all real numbers.
  • D 𝑓 ( 1 ) = 0
  • E 𝑓 1 2 3 = 1

Q21:

Using the graph shown which represents the function 𝑓(𝑥)=𝑥−4𝑥+2, evaluate 𝑓(−2).

  • A0
  • B − 2
  • C − 4
  • Dundefined

Q22:

The given graph represents a function. What would be the value of the output for an input of 5?

Q23:

If the following graph represents the function 𝑓(𝑥)=𝑥+3, determine 𝑓(1).

Q24:

Find the output, 𝑦, of the function represented by the given graph when its input is 2.

Q25:

If the following graph represents the function 𝑓(𝑥)=(𝑥+1), determine 𝑓(−1).

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