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Worksheet: Evaluating Linear Functions

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 π‘₯ + 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:

Select the linear function whose graph is contained in the line 2 𝑦 βˆ’ 3 π‘₯ + 7 = 0 .

  • A 𝑓 ( π‘₯ ) = 3 π‘₯ + 7 2
  • B 𝑓 = { ( βˆ’ 3 , βˆ’ 8 ) , ( βˆ’ 1 , βˆ’ 5 ) , ( 1 , βˆ’ 2 ) , ( 3 , 1 ) }
  • Cthe line with intercepts ο€Ό βˆ’ 7 3 , 0  and ο€Ό 0 , βˆ’ 7 2 
  • D 𝑓 ( 2 ) = βˆ’ 1 0 , 𝑓 ( 𝑛 + 1 ) = 𝑓 ( 𝑛 ) βˆ’ 3 2

Q3:

Find the coordinates of the points 𝑓 ( 2 ) , 𝑓 ( 1 7 ) , and 𝑓 ( 3 1 ) given 𝑓 ( π‘₯ ) = π‘₯ + 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 )

Q4:

Given that satisfies the relation , find the value of .

Q5:

Evaluate 𝑓 ( 4 βˆ’ π‘₯ ) , given that 𝑓 ( π‘₯ ) = 3 π‘₯ + 7 .

  • A 𝑓 ( 4 βˆ’ π‘₯ ) = 3 π‘₯ + 1 2
  • B 𝑓 ( 4 βˆ’ π‘₯ ) = 3 π‘₯ + 7
  • C 𝑓 ( 4 βˆ’ π‘₯ ) = βˆ’ 3 π‘₯ + 1 2
  • D 𝑓 ( 4 βˆ’ π‘₯ ) = βˆ’ 3 π‘₯ + 1 9
  • E 𝑓 ( 4 βˆ’ π‘₯ ) = 3 π‘₯ + 1 8

Q6:

Evaluate 𝑓 ( 2 ) , given that 𝑓 ( π‘₯ ) = 3 π‘₯ + 7 .

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

Q7:

Consider a linear function 𝑓 ( π‘₯ ) = π‘š π‘₯ + 𝑐 .

Give an expression for 𝑓 ( π‘₯ + Ξ” π‘₯ ) βˆ’ 𝑓 ( π‘₯ ) .

  • A π‘š
  • B π‘š Ξ” π‘₯ + 2 𝑐
  • C 𝑐
  • D π‘š Ξ” π‘₯
  • E Ξ” π‘₯

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

  • AA linear function grows by a constant value ( π‘š Ξ” π‘₯ ) over a constant interval Ξ” π‘₯ .
  • BA linear function grows by a constant value ( π‘š Ξ” π‘₯ + 𝑐 ) over a constant interval Ξ” π‘₯ .
  • CA linear function grows by a constant value ( Ξ” π‘₯ ) over a constant interval Ξ” π‘₯ .
  • DA linear function grows by a constant value ( π‘š ) over a constant interval Ξ” π‘₯ .
  • EA linear function grows by a constant value ( π‘š Ξ” π‘₯ + 2 𝑐 ) over a constant interval Ξ” π‘₯ .

Q8:

Which of the following satisfies the relation π‘₯ βˆ’ 𝑦 = βˆ’ 1 0 ?

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

Q9:

Given that ( 1 , π‘Ž ) satisfies the relation 𝑦 βˆ’ 4 π‘₯ = 7 , find the value of π‘Ž .

Q10:

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 ]

Q11:

Find 𝑏 given 𝑓 ( π‘₯ ) = 5 π‘₯ + 𝑏 where 𝑓 ( 5 ) = 1 7 .

Q12:

Evaluate 𝑓 ( βˆ’ π‘₯ ) , given that 𝑓 ( π‘₯ ) = 3 π‘₯ + 7 .

  • A 𝑓 ( βˆ’ π‘₯ ) = 3 π‘₯ βˆ’ 7
  • B 𝑓 ( βˆ’ π‘₯ ) = 3 π‘₯ + 7
  • C 𝑓 ( βˆ’ π‘₯ ) = 3 + 7 π‘₯
  • D 𝑓 ( βˆ’ π‘₯ ) = βˆ’ 3 π‘₯ + 7
  • E 𝑓 ( βˆ’ π‘₯ ) = 3 βˆ’ 7 π‘₯

Q13:

Given the function 𝑦 = 7 + 2 π‘₯ , what is the output of this function when the input is 4?

Q14:

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

  • A 𝑦 = 3 π‘₯ + 4
  • B 𝑦 = 4 π‘₯ + 5
  • C 𝑦 = 4 π‘₯ + 3
  • D 𝑦 = 2 π‘₯ + 3
  • E 𝑦 = 3 π‘₯ + 3

Q15:

Which of the following pairs all satisfy the relation π‘₯ βˆ’ 𝑦 = βˆ’ 1 3 ?

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

Q16:

Given that ( βˆ’ 7 , βˆ’ 3 ) satisfies the relation 3 π‘₯ + 𝑏 𝑦 = βˆ’ 3 , find the value of 𝑏 .

Q17:

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 𝑑 the total selling price of both types of books.

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

Q18:

Fill in the missing values given that the following pairs satisfy the relation 𝑦 = 3 π‘₯ βˆ’ 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

Q19:

If 𝑔 ∢ { 9 , 1 0 , 1 1 , 1 2 , 1 3 } ⟢ β„€ + , where 𝑔 ( π‘₯ ) = 1 7 π‘₯ βˆ’ 1 8 and 𝑔 ( π‘˜ ) = 2 0 3 , find the value of π‘˜ .

Q20:

Given that ( 0 , 2 π‘š ) satisfies the relation 𝑦 = 5 π‘₯ βˆ’ 8 , find the value of π‘š .

Q21:

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

  • A 3 π‘₯ βˆ’ 𝑦 = βˆ’ 1 7
  • B 4 π‘₯ + 𝑦 = βˆ’ 1 8
  • C 5 π‘₯ + 3 𝑦 = βˆ’ 1 9
  • D 5 π‘₯ + 2 𝑦 = 0
  • E 5 π‘₯ + 𝑦 = βˆ’ 2 3

Q22:

Evaluate 𝑓 ( 𝑇 ) , given that 𝑓 ( π‘₯ ) = 3 π‘₯ + 7 .

  • A 𝑓 ( 𝑇 ) = 3 𝑦 + 7
  • B 𝑓 ( 𝑇 ) = 3 π‘₯ + 7
  • C 𝑓 ( 𝑇 ) = 𝑇 + 3
  • D 𝑓 ( 𝑇 ) = 3 𝑇 + 7
  • E 𝑓 ( 𝑇 ) = 3 + 7 𝑇

Q23:

Answer the following questions for the functions 𝑦 = 3 π‘₯ βˆ’ 1 and 𝑦 = βˆ’ 1 2 π‘₯ + 5 2 .

Complete the table of values for 𝑦 = 3 π‘₯ βˆ’ 1 .

π‘₯ βˆ’ 2 βˆ’ 1 0 1 2
𝑦
  • A βˆ’ 5 , βˆ’ 2 , βˆ’ 1 , 4 , 7
  • B βˆ’ 6 , βˆ’ 3 , 3 , 3 , 6
  • C βˆ’ 7 , βˆ’ 4 , 3 , 2 , 5
  • D βˆ’ 7 , βˆ’ 4 , βˆ’ 1 , 2 , 5
  • E βˆ’ 6 , βˆ’ 3 , βˆ’ 1 , 3 , 6

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

π‘₯ βˆ’ 2 βˆ’ 1 0 1 2
𝑦
  • A 7 2 , 3 , 5 2 , 2 , 3 2
  • B 7 2 , 3 , βˆ’ 1 2 , 2 , 3 2
  • C 3 2 , 2 , 5 2 , 3 , 7 2
  • D 1 , 1 2 , 5 2 , βˆ’ 1 2 , βˆ’ 1
  • E 1 , 1 2 , βˆ’ 1 2 , βˆ’ 1 2 , βˆ’ 1

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

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

Q24:

Find the range of 𝑓 given 𝑓 ( π‘₯ ) = βˆ’ 2 π‘₯ βˆ’ 3 where π‘₯ ∈ { 5 , 1 0 } .

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

Q25:

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

  • A 2 π‘₯ + 𝑦 = βˆ’ 2
  • B 2 π‘₯ βˆ’ 𝑦 = 2
  • C π‘₯ + 2 𝑦 = βˆ’ 2
  • D 2 π‘₯ βˆ’ 𝑦 = βˆ’ 2
  • E π‘₯ + 2 𝑦 = 6

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