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.

Input0245
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.

  • A𝑓(2)=3
  • B𝑓(2)=13
  • C𝑓(2)=12
  • D𝑓(2)=10
  • E𝑓(2)=7

Q3:

Evaluate 𝑓(𝑥), given that 𝑓(𝑥)=3𝑥+7.

  • A𝑓(𝑥)=37𝑥
  • B𝑓(𝑥)=3𝑥+7
  • C𝑓(𝑥)=3+7𝑥
  • D𝑓(𝑥)=3𝑥+7
  • E𝑓(𝑥)=3𝑥7

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(16,6)
  • C(9,1)
  • D(12,2)
  • E(5,15)

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)?

  • A𝑦=4𝑥+3
  • B𝑦=2𝑥+3
  • C𝑦=4𝑥+5
  • D𝑦=3𝑥+4
  • E𝑦=3𝑥+3

Q10:

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

  • A(21,8),(19,6),(17,4),(8,5)
  • B(8,5),(6,7),(4,9),(8,21)
  • C(5,8),(7,6),(9,4),(8,21)
  • D(5,8),(7,6),(9,4),(21,8)
  • E(21,8),(19,6),(17,4),(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,).

  • A26,35,41,50
  • B103,133,5,6
  • C24,33,39,48
  • D22,31,37,46
  • E2,3,113,143

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?

  • A5𝑥+𝑦=23
  • B5𝑥+2𝑦=0
  • C5𝑥+3𝑦=19
  • D3𝑥𝑦=17
  • E4𝑥+𝑦=18

Q15:

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

  • A2𝑥𝑦=2
  • B𝑥+2𝑦=6
  • C2𝑥𝑦=2
  • D𝑥+2𝑦=2
  • E2𝑥+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
  • B𝑓(2)=10, 𝑓(𝑛+1)=𝑓(𝑛)32
  • C𝑓(𝑥)=3𝑥+72
  • D𝑓={(3,8),(1,5),(1,2),(3,1)}

Q17:

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

  • A(14,2),(43,17),(29,31)
  • B(14,2),(29,17),(43,31)
  • C(2,29),(17,14),(31,43)
  • D(2,14),(17,29),(31,43)

Q18:

Evaluate 𝑓(4𝑥), given that 𝑓(𝑥)=3𝑥+7.

  • A𝑓(4𝑥)=3𝑥+19
  • B𝑓(4𝑥)=3𝑥+12
  • C𝑓(4𝑥)=3𝑥+18
  • D𝑓(4𝑥)=3𝑥+7
  • E𝑓(4𝑥)=3𝑥+12

Q19:

Consider a linear function 𝑓(𝑥)=𝑚𝑥+𝑐.

Give an expression for 𝑓(𝑥+Δ𝑥)𝑓(𝑥).

  • A𝑚
  • B𝑚Δ𝑥+2𝑐
  • C𝑐
  • DΔ𝑥
  • E𝑚Δ𝑥

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[160,1,200]
  • B[80,120]
  • C[1,600,2,400]
  • D[0,1,600]

Q21:

Evaluate 𝑓(𝑇), given that 𝑓(𝑥)=3𝑥+7.

  • A𝑓(𝑇)=3𝑦+7
  • B𝑓(𝑇)=3𝑥+7
  • C𝑓(𝑇)=3𝑇+7
  • D𝑓(𝑇)=3+7𝑇
  • E𝑓(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.

𝑥21012
𝑦
  • A7,4,1,2,5
  • B5,2,1,4,7
  • C6,3,1,3,6
  • D6,3,3,3,6
  • E7,4,3,2,5

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

𝑥21012
𝑦
  • A1,12,52,12,1
  • B72,3,12,2,32
  • C32,2,52,3,72
  • D1,12,12,12,1
  • E72,3,52,2,32

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.

  • A𝑡=11𝑑15𝑣, $43.00
  • B𝑡=11𝑑+15𝑣, $133.00
  • C𝑡=15𝑑+11𝑣, $153.00
  • D𝑡=8𝑑+3𝑣, $133.00
  • E𝑡=15𝑑11𝑣, $87.00

Q24:

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

  • A{23,13}
  • B{20,10}
  • C{20,2}
  • 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),(10,21), range ={9,6,3,}
  • B(6,1),(3,4),(21,10), range ={6,3,21}
  • C(1,12),(4,21),(10,39), range ={9,12,15,}
  • D(12,1),(21,4),(39,10), range ={12,21,39}

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.