Worksheet: Linear Functions

Download

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)=3−7𝑥
  • B𝑓(−𝑥)=−3𝑥+7
  • C𝑓(−𝑥)=3+7𝑥
  • D𝑓(−𝑥)=3𝑥+7
  • E𝑓(−𝑥)=3𝑥−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}⟶ℤ, where 𝑔(𝑥)=17𝑥−18 and 𝑔(𝑘)=203, find the value of 𝑘.

Q6:

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

Q7:

Which of the following satisfies the relation 𝑥−𝑦=−10?

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

Q8:

Given that (1,𝑎) satisfies the relation 𝑦−4𝑥=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 𝑥−𝑦=−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=3𝑥−2: (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=5𝑥−8, 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
  • D3𝑥−𝑦=−17
  • E4𝑥+𝑦=−18

Q15:

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

  • A2𝑥−𝑦=2
  • B𝑥+2𝑦=6
  • C2𝑥−𝑦=−2
  • D𝑥+2𝑦=−2
  • E2𝑥+𝑦=−2

Q16:

Select the linear function whose graph is contained in the line 2𝑦−3𝑥+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(4−𝑥), given that 𝑓(𝑥)=3𝑥+7.

  • A𝑓(4−𝑥)=−3𝑥+19
  • B𝑓(4−𝑥)=3𝑥+12
  • C𝑓(4−𝑥)=3𝑥+18
  • D𝑓(4−𝑥)=3𝑥+7
  • E𝑓(4−𝑥)=−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 80∘C and 120∘C, 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=3𝑥−1 and 𝑦=−12𝑥+52.

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

𝑥−2−1012
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−2−1012
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=11𝑑−15𝑣, $43.00
  • B𝑡=11𝑑+15𝑣, $133.00
  • C𝑡=15𝑑+11𝑣, $153.00
  • D𝑡=8𝑑+3𝑣, $133.00
  • E𝑡=15𝑑−11𝑣, $87.00

Q24:

Find the range of 𝑓 given 𝑓(𝑥)=−2𝑥−3 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.