Worksheet: Comparing Rates of Change

In this worksheet, we will practice comparing the rates of change of functions represented by graphs and tables.


Which of the following functions increases at a higher rate?

  • A
  • B


Determine which of the given functions has a greater rate of change.


𝑥 0 1 2 3 4
𝑦 2 0 2 4 6

(b) 𝑦 = 3 𝑥 + 5

  • A(a)
  • BThey have the same rate of change.
  • C(b)


Determine which of the given functions has a greater rate of change.

(a) 𝑦 = 5 𝑥 + 8

(b) a function where the input is multiplied by 2

  • AThey have the same rate of change.
  • Bb
  • Ca


Consider the following graphs of linear functions, all of which have the same scales on the two axes.

List the graphs in order of increasing rate of change of 𝑦 with respect to 𝑥 .

  • A (c), (b), (a), (d)
  • B(b), (c), (d), (a)
  • C (b), (c), (a), (d)
  • D (a), (d), (c), (b)
  • EThis cannot be determined without more information.


Victoria says that the ratios of protein to carbohydrate in the two samples are equivalent. Is she correct?

Sample 1 Sample 2
Protein (g) 4 36
Carbohydrate (g) 7 63
  • Ayes
  • Bno


Which of the following functions has a greater rate of change?


(b) 𝑦 = 2 𝑥 9

  • Ab
  • Ba
  • CThey have the same rate of change.


A customer is looking for the best deal on a recurring order. Which deal should he take?

  • A$20 for every 5 lb
  • B$42 for every 7 lb
  • C$16 for every 8 lb
  • D$15 for every 10 lb
  • E$15 for every 3 lb


A car manufacturer claims that the fuel consumption of one of their cars is 42 mpg (miles per gallon). Chloe measured the distance she covered with different volumes of fuel. She plotted her results and drew a line of best fit.

Did her car consume more or less fuel than the manufacturer had claimed?

  • Athe same
  • Bmore
  • Cless


On average, 900 grams of chicken has about 990 calories, while 200 grams of beef has about 386 calories. Which meat provides more energy per gram?

  • AChicken
  • BBeef


Jennifer wants to burn an extra 2 0 0 0 calories a week. She can choose between the following exercise classes.

Class Duration Calories Burned
A 1 1 4 hours 600
B 45 minutes 375
C 1 hour 400

Which class burns the most calories per hour?

  • AC
  • BA
  • CB

How long would she have to spend in that class to reach her weekly goal?

  • A 3 1 3 hours
  • B 5 1 3 hours
  • C 5 hours
  • D 4 1 6 hours
  • E 4 hours

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