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(π‘₯)=βˆ’19π‘₯βˆ’16?

  • A(βˆ’206,βˆ’16)
  • B(βˆ’206,10)
  • C(10,βˆ’16)
  • D(10,βˆ’206)

Q2:

Find 𝑦, given the point (βˆ’2,𝑦) lies on the function 𝑓(π‘₯)=βˆ’6π‘₯βˆ’10π‘₯+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.

Q4:

Find 𝑓(5)+𝑓(βˆ’8) given the function 𝑓(π‘₯)=βˆ’11.

Q5:

Given that the function 𝑓(π‘₯)=βˆ’2π‘₯+10π‘₯βˆ’2, where π‘“βˆΆβ„β†’β„, determine 𝑓(3).

Q6:

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

Q7:

Find the value of 4π‘“ο€»βˆš3ο‡βˆ’4π‘”ο€»βˆš3 given the function 𝑓(π‘₯)=π‘₯+7π‘₯ and the function 𝑔(π‘₯)=7π‘₯βˆ’4.

Q8:

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

π‘₯βˆ’2βˆ’1012
𝑦
  • Aβˆ’16,βˆ’5,1,5,16
  • Bβˆ’16,βˆ’5,0,1,8
  • Cβˆ’8,βˆ’1,0,1,8
  • Dβˆ’8,βˆ’1,1,5,16
  • E16,5,0,1,8

Q9:

Complete the given table of values for the function 𝑦=15βˆ’7π‘₯+8π‘₯.

π‘₯βˆ’2βˆ’1012
𝑦
  • Aβˆ’29,0,15,16,3
  • B27,14,8,14,βˆ’3
  • C59,30,15,16,3
  • Dβˆ’29,0,8,14,βˆ’3
  • E27,14,15,16,3

Q10:

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

  • A𝑦=2
  • B𝑦=βˆ’1
  • C𝑦=4
  • D𝑦=10
  • E𝑦=βˆ’4

Q11:

If 𝑓(π‘₯)=7π‘₯βˆ’4π‘₯βˆ’5, find 𝑓4+√6ο‡βˆ’π‘“ο€»4βˆ’βˆš6.

  • Aβˆ’104√6+266
  • B104√6+266
  • C104√6
  • Dβˆ’104√6
  • E266

Q12:

Find 𝑦, given the point (βˆ’3,𝑦) lies on the function 𝑓(π‘₯)=βˆ’7π‘₯+π‘₯βˆ’8.

Q13:

Which of the following set of coordinates lies on 𝑓(π‘₯)=13π‘₯βˆ’13?

  • A(65,βˆ’13)
  • B(65,6)
  • C(6,βˆ’13)
  • D(6,65)

Q14:

Which of the following is NOT a point on the curve 𝑓(π‘₯)=π‘₯+3π‘₯βˆ’5?

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

Q15:

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

What sequence is produced by inputing the positive integers into 𝑔(π‘₯)=2π‘₯βˆ’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 β„Ž(π‘₯)=(βˆ’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,βˆ’2,0,βˆ’2,0}

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

  • A𝑓(π‘₯)=1βˆ’(βˆ’1)2
  • B𝑓(π‘₯)=2+(βˆ’1)2
  • C𝑓(π‘₯)=12βˆ’(βˆ’1)
  • D𝑓(π‘₯)=1+(βˆ’1)
  • E𝑓(π‘₯)=2βˆ’(βˆ’1)

Q16:

Given a function 𝑓, the meaning of 𝑓(π‘Žβˆ’1) is β€œthe output when the input is 1 less than π‘Ž.” 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
  • C𝑏+3 times the output
  • D𝑏+3 times the input
  • Ethe input when the ouput is 3 more than 𝑏

𝑓(𝑠)βˆ’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(3βˆ’π‘₯)

  • Athe output when the input is π‘₯ less than 3
  • Bthe output when the input is π‘₯ more than 3
  • Cthe input when the ouput is π‘₯ less than 3
  • Dthe input when the ouput is π‘₯ more than 3

𝑓(𝑏)βˆ’π‘“(π‘Ž)

  • Athe change in input when the output changes from 𝑏 to π‘Ž
  • Bthe change in output when the input changes from π‘Ž to 𝑏
  • Cthe change in output when the input changes from 𝑏 to π‘Ž
  • Dthe change in input when the output changes from π‘Ž to 𝑏

𝑓(3𝑑)

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

𝑓(π‘Ž)

  • Athe result of raising the input at output π‘Ž to the 𝑏th power
  • Bthe result of raising the output at input 𝑏 to the π‘Žth power
  • Cthe result of raising the input at output 𝑏 to the π‘Žth power
  • Dthe result of raising the output at input π‘Ž to the 𝑏th power

Q17:

The function 𝐷(𝑑) records Benjamin’s distance in kilometers from his home 𝑑 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(60)=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(23)=𝐷(32)

  • 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(16)>𝐷(12)

  • 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(π‘Ž)=1.2

  • AAt time π‘Ž, Benjamin is 1.2 km from home.
  • BAt time 1.2 minutes, Benjamin is 2π‘Ž km from home.
  • CAt time 1.2 minutes, Benjamin is π‘Ž km from home.
  • DAt time π‘Ž, Benjamin is 2.4 km from home.

𝐷(13)=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(𝑑) be the temperature of the potato 𝑑 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.

  • A𝑓(0)>20
  • B𝑓(0)=20
  • C𝑓(0)<20
  • D𝑓(20)>0
  • E𝑓(20)=0

The potato was hotter at 10 minutes than at 5.

  • A𝑓(5)<𝑓(10)
  • B𝑓(5)=𝑓(10)
  • C𝑓(5)>𝑓(10)

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

  • A𝑓(40)<𝑓(45)
  • B𝑓(40)=𝑓(45)
  • C𝑓(40)>𝑓(45)

Q19:

Find β„Ž(2), if β„Ž(π‘₯)=𝑓(π‘₯)𝑔(π‘₯) and 𝑓(π‘₯)=π‘₯βˆ’π‘₯+1, 𝑔(π‘₯)=π‘₯+1.

Q20:

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

  • AThe range of 𝑓 is the set of all integers.
  • B𝑓(βˆ’0.5)=βˆ’1
  • CThe domain of 𝑓 is assumed to be the set of all real numbers.
  • D𝑓(1)=0
  • E𝑓123=1

Q21:

Using the graph shown which represents the function 𝑓(π‘₯)=π‘₯βˆ’4π‘₯+2, evaluate 𝑓(βˆ’2).

  • A0
  • Bβˆ’2
  • Cβˆ’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(π‘₯)=π‘₯+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(π‘₯)=(π‘₯+1), determine 𝑓(βˆ’1).

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