Worksheet: Linear Functions

In this worksheet, we will practice identifying, writing, and evaluating a linear function and completing its function table.

Q1:

Fill in the input-output table for the function 𝑦=5𝑥+3.

Input 0 2 4 5
Output
  • A3, 13, 23, 28
  • B3, 12, 23, 28
  • C0, 12, 23, 28
  • D3, 13, 23, 27
  • E0, 13, 23, 28

Q2:

Evaluate 𝑓(2), given that 𝑓(𝑥)=3𝑥+7.

  • A 𝑓 ( 2 ) = 3
  • B 𝑓 ( 2 ) = 1 3
  • C 𝑓 ( 2 ) = 1 2
  • D 𝑓 ( 2 ) = 1 0
  • E 𝑓 ( 2 ) = 7

Q3:

Evaluate 𝑓(𝑥), given that 𝑓(𝑥)=3𝑥+7.

  • A 𝑓 ( 𝑥 ) = 3 7 𝑥
  • B 𝑓 ( 𝑥 ) = 3 𝑥 + 7
  • C 𝑓 ( 𝑥 ) = 3 + 7 𝑥
  • D 𝑓 ( 𝑥 ) = 3 𝑥 + 7
  • E 𝑓 ( 𝑥 ) = 3 𝑥 7

Q4:

Given the function 𝑦=7+2𝑥, what is the output of this function when the input is 4?

Q5:

If 𝑔{9,10,11,12,13}, where 𝑔(𝑥)=17𝑥18 and 𝑔(𝑘)=203, find the value of 𝑘.

Q6:

Given that (𝑘,2𝑘) satisfies the relation 𝑥2𝑦=3, find the value of 𝑘.

Q7:

Which of the following satisfies the relation 𝑥𝑦=10?

  • A ( 2 , 2 )
  • B ( 1 6 , 6 )
  • C ( 9 , 1 )
  • D ( 1 2 , 2 )
  • E ( 5 , 1 5 )

Q8:

Given that (1,𝑎) satisfies the relation 𝑦4𝑥=7, find the value of 𝑎.

Q9:

Which of the following relations is satisfied by both the point (1,1) and the point (0,3)?

  • A 𝑦 = 4 𝑥 + 3
  • B 𝑦 = 2 𝑥 + 3
  • C 𝑦 = 4 𝑥 + 5
  • D 𝑦 = 3 𝑥 + 4
  • E 𝑦 = 3 𝑥 + 3

Q10:

Which of the following pairs all satisfy the relation 𝑥𝑦=13?

  • A ( 2 1 , 8 ) , ( 1 9 , 6 ) , ( 1 7 , 4 ) , ( 8 , 5 )
  • B ( 8 , 5 ) , ( 6 , 7 ) , ( 4 , 9 ) , ( 8 , 2 1 )
  • C ( 5 , 8 ) , ( 7 , 6 ) , ( 9 , 4 ) , ( 8 , 2 1 )
  • D ( 5 , 8 ) , ( 7 , 6 ) , ( 9 , 4 ) , ( 2 1 , 8 )
  • E ( 2 1 , 8 ) , ( 1 9 , 6 ) , ( 1 7 , 4 ) , ( 5 , 8 )

Q11:

Given that (7,3) satisfies the relation 3𝑥+𝑏𝑦=3, find the value of 𝑏.

Q12:

Fill in the missing values given that the following pairs satisfy the relation 𝑦=3𝑥2: (8,), (11,), (13,), and (16,).

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

Q13:

Given that (0,2𝑚) satisfies the relation 𝑦=5𝑥8, find the value of 𝑚.

Q14:

Which of the following relations does the point (5,2) not satisfy?

  • A 5 𝑥 + 𝑦 = 2 3
  • B 5 𝑥 + 2 𝑦 = 0
  • C 5 𝑥 + 3 𝑦 = 1 9
  • D 3 𝑥 𝑦 = 1 7
  • E 4 𝑥 + 𝑦 = 1 8

Q15:

Which of the following does the point (2,2) satisfy?

  • A 2 𝑥 𝑦 = 2
  • B 𝑥 + 2 𝑦 = 6
  • C 2 𝑥 𝑦 = 2
  • D 𝑥 + 2 𝑦 = 2
  • E 2 𝑥 + 𝑦 = 2

Q16:

Select the linear function whose graph is contained in the line 2𝑦3𝑥+7=0.

  • Athe line with intercepts 73,0 and 0,72
  • B 𝑓 = { ( 3 , 8 ) , ( 1 , 5 ) , ( 1 , 2 ) , ( 3 , 1 ) }
  • C 𝑓 ( 𝑥 ) = 3 𝑥 + 7 2
  • D 𝑓 ( 2 ) = 1 0 , 𝑓 ( 𝑛 + 1 ) = 𝑓 ( 𝑛 ) 3 2

Q17:

Find the coordinates of the points 𝑓(2), 𝑓(17), and 𝑓(31) given 𝑓(𝑥)=𝑥+12.

  • A ( 1 4 , 2 ) , ( 4 3 , 1 7 ) , ( 2 9 , 3 1 )
  • B ( 1 4 , 2 ) , ( 2 9 , 1 7 ) , ( 4 3 , 3 1 )
  • C ( 2 , 2 9 ) , ( 1 7 , 1 4 ) , ( 3 1 , 4 3 )
  • D ( 2 , 1 4 ) , ( 1 7 , 2 9 ) , ( 3 1 , 4 3 )

Q18:

Evaluate 𝑓(4𝑥), given that 𝑓(𝑥)=3𝑥+7.

  • A 𝑓 ( 4 𝑥 ) = 3 𝑥 + 1 9
  • B 𝑓 ( 4 𝑥 ) = 3 𝑥 + 1 2
  • C 𝑓 ( 4 𝑥 ) = 3 𝑥 + 1 8
  • D 𝑓 ( 4 𝑥 ) = 3 𝑥 + 7
  • E 𝑓 ( 4 𝑥 ) = 3 𝑥 + 1 2

Q19:

Consider a linear function 𝑓(𝑥)=𝑚𝑥+𝑐.

Give an expression for 𝑓(𝑥+Δ𝑥)𝑓(𝑥).

  • A 𝑚
  • B 𝑚 Δ 𝑥 + 2 𝑐
  • C 𝑐
  • D Δ 𝑥
  • E 𝑚 Δ 𝑥

What can you conclude about the way a linear function grows?

  • AA linear function grows by a constant value (𝑚Δ𝑥+2𝑐) over a constant interval Δ𝑥.
  • BA linear function grows by a constant value (Δ𝑥) over a constant interval Δ𝑥.
  • CA linear function grows by a constant value (𝑚) over a constant interval Δ𝑥.
  • DA linear function grows by a constant value (𝑚Δ𝑥) over a constant interval Δ𝑥.
  • EA linear function grows by a constant value (𝑚Δ𝑥+𝑐) over a constant interval Δ𝑥.

Q20:

In chemistry, the volume of a certain gas is given by 𝑉=20𝑇, where 𝑇 is temperature in degrees Celsius. If the temperature varies between 80C and 120C, find the interval that describes the corresponding volume values.

  • A [ 1 6 0 , 1 , 2 0 0 ]
  • B [ 8 0 , 1 2 0 ]
  • C [ 1 , 6 0 0 , 2 , 4 0 0 ]
  • D [ 0 , 1 , 6 0 0 ]

Q21:

Evaluate 𝑓(𝑇), given that 𝑓(𝑥)=3𝑥+7.

  • A 𝑓 ( 𝑇 ) = 3 𝑦 + 7
  • B 𝑓 ( 𝑇 ) = 3 𝑥 + 7
  • C 𝑓 ( 𝑇 ) = 3 𝑇 + 7
  • D 𝑓 ( 𝑇 ) = 3 + 7 𝑇
  • E 𝑓 ( 𝑇 ) = 𝑇 + 3

Q22:

Answer the following questions for the functions 𝑦=3𝑥1 and 𝑦=12𝑥+52.

Complete the table of values for 𝑦=3𝑥1.

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

Complete the table of values for 𝑦=12𝑥+52.

𝑥 2 1 0 1 2
𝑦
  • A 1 , 1 2 , 5 2 , 1 2 , 1
  • B 7 2 , 3 , 1 2 , 2 , 3 2
  • C 3 2 , 2 , 5 2 , 3 , 7 2
  • D 1 , 1 2 , 1 2 , 1 2 , 1
  • E 7 2 , 3 , 5 2 , 2 , 3 2

Use the tables of values to determine the intersection point of the two graphs.

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

Q23:

A bookstore sells used paperback books for $11.00 each and used hardcover books for $15.00 each. Find a function rule that shows the total selling price of both types of books, and then determine the price of 8 paperback and 3 hardcover books. Let 𝑑 represent the number of paperback books, 𝑣 the number of hardcover books, and 𝑡 the total selling price of both types of books.

  • A 𝑡 = 1 1 𝑑 1 5 𝑣 , $43.00
  • B 𝑡 = 1 1 𝑑 + 1 5 𝑣 , $133.00
  • C 𝑡 = 1 5 𝑑 + 1 1 𝑣 , $153.00
  • D 𝑡 = 8 𝑑 + 3 𝑣 , $133.00
  • E 𝑡 = 1 5 𝑑 1 1 𝑣 , $87.00

Q24:

Find the range of 𝑓 given 𝑓(𝑥)=2𝑥3 where 𝑥{5,10}.

  • A { 2 3 , 1 3 }
  • B { 2 0 , 1 0 }
  • C { 2 0 , 2 }
  • D { 2 , 7 }

Q25:

Find 𝑡(1), 𝑡(4) and 𝑡(10) in coordinate form and the range of the function 𝑡(𝑥)=3𝑥+9.

  • A ( 1 , 6 ) , ( 4 , 3 ) , ( 1 0 , 2 1 ) , range ={9,6,3,}
  • B ( 6 , 1 ) , ( 3 , 4 ) , ( 2 1 , 1 0 ) , range ={6,3,21}
  • C ( 1 , 1 2 ) , ( 4 , 2 1 ) , ( 1 0 , 3 9 ) , range ={9,12,15,}
  • D ( 1 2 , 1 ) , ( 2 1 , 4 ) , ( 3 9 , 1 0 ) , range ={12,21,39}

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