Worksheet: Evaluating Linear Functions

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In this worksheet, we will practice evaluating a linear function at a certain point, completing a function table, and using function tables to organize input-output values.

Q1:

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

Input 0 2 4 5
Output … … … …
  • A0, 13, 23, 28
  • B3, 12, 23, 28
  • C0, 12, 23, 28
  • D3, 13, 23, 28
  • E3, 13, 23, 27

Q2:

Evaluate 𝑓 ( 2 ) , given that 𝑓 ( 𝑥 ) = 3 𝑥 + 7 .

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

Q3:

Evaluate 𝑓 ( − 𝑥 ) , given that 𝑓 ( 𝑥 ) = 3 𝑥 + 7 .

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

Q4:

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

Q5:

If 𝑔 ∶ { 9 , 1 0 , 1 1 , 1 2 , 1 3 } ⟶ ℤ , where 𝑔 ( 𝑥 ) = 1 7 𝑥 − 1 8 and 𝑔 ( 𝑘 ) = 2 0 3 , find the value of 𝑘 .

Q6:

Given that satisfies the relation , find the value of .

Q7:

Which of the following satisfies the relation 𝑥 − 𝑦 = − 1 0 ?

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

Q8:

Given that ( 1 , 𝑎 ) satisfies the relation 𝑦 − 4 𝑥 = 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 = 3 𝑥 + 4
  • B 𝑦 = 4 𝑥 + 5
  • C 𝑦 = 4 𝑥 + 3
  • D 𝑦 = 2 𝑥 + 3
  • E 𝑦 = 3 𝑥 + 3

Q10:

Which of the following pairs all satisfy the relation 𝑥 − 𝑦 = − 1 3 ?

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

Q11:

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

Q12:

Fill in the missing values given that the following pairs satisfy the relation 𝑦 = 3 𝑥 − 2 : ( 8 , ) , ( 1 1 , ) , ( 1 3 , ) , and ( 1 6 , ) .

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

Q13:

Given that ( 0 , 2 𝑚 ) satisfies the relation 𝑦 = 5 𝑥 − 8 , find the value of 𝑚 .

Q14:

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

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

Q15:

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

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

Q16:

Select the linear function whose graph is contained in the line 2 𝑦 − 3 𝑥 + 7 = 0 .

  • A 𝑓 ( 𝑥 ) = 3 𝑥 + 7 2
  • B 𝑓 = { ( − 3 , − 8 ) , ( − 1 , − 5 ) , ( 1 , − 2 ) , ( 3 , 1 ) }
  • Cthe line with intercepts − 7 3 , 0 and 0 , − 7 2
  • D 𝑓 ( 2 ) = − 1 0 , 𝑓 ( 𝑛 + 1 ) = 𝑓 ( 𝑛 ) − 3 2

Q17:

Find the coordinates of the points 𝑓 ( 2 ) , 𝑓 ( 1 7 ) , and 𝑓 ( 3 1 ) given 𝑓 ( 𝑥 ) = 𝑥 + 1 2 .

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

Q18:

Evaluate 𝑓 ( 4 − 𝑥 ) , given that 𝑓 ( 𝑥 ) = 3 𝑥 + 7 .

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

Q19:

Consider a linear function 𝑓 ( 𝑥 ) = 𝑚 𝑥 + 𝑐 .

Give an expression for 𝑓 ( 𝑥 + Δ 𝑥 ) − 𝑓 ( 𝑥 ) .

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

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

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

Q20:

In chemistry, the volume of a certain gas is given by 𝑉 = 2 0 𝑇 , where 𝑇 is temperature in degrees Celsius. If the temperature varies between 8 0 ∘ C and 1 2 0 ∘ C , find the interval that describes the corresponding volume values.

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

Q21:

Evaluate 𝑓 ( 𝑇 ) , given that 𝑓 ( 𝑥 ) = 3 𝑥 + 7 .

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

Q22:

Answer the following questions for the functions 𝑦 = 3 𝑥 − 1 and 𝑦 = − 1 2 𝑥 + 5 2 .

Complete the table of values for 𝑦 = 3 𝑥 − 1 .

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

Complete the table of values for 𝑦 = − 1 2 𝑥 + 5 2 .

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

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 , 0 )
  • E ( − 2 , − 1 )

Q23:

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

Q24:

Find the range of 𝑓 given 𝑓 ( 𝑥 ) = − 2 𝑥 − 3 where 𝑥 ∈ { 5 , 1 0 } .

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

Q25:

Find 𝑡 ( 1 ) , 𝑡 ( 4 ) and 𝑡 ( 1 0 ) in coordinate form and the range of the function 𝑡 ( 𝑥 ) = 3 𝑥 + 9 .

  • A ( 1 , − 6 ) , ( 4 , 3 ) , ( 1 0 , 2 1 ) , range = { − 9 , − 6 , − 3 , … }
  • B ( 1 2 , 1 ) , ( 2 1 , 4 ) , ( 3 9 , 1 0 ) , range = { 1 2 , 2 1 , 3 9 }
  • C ( − 6 , 1 ) , ( 3 , 4 ) , ( 2 1 , 1 0 ) , range = { − 6 , 3 , 2 1 }
  • D ( 1 , 1 2 ) , ( 4 , 2 1 ) , ( 1 0 , 3 9 ) , range = { 9 , 1 2 , 1 5 , … }

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