Worksheet: Comparing Rates of Change

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

Q1:

Which of the following functions increases at a higher rate?

  • A
  • B

Q2:

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

(a)

𝑥 0 1 2 3 4
𝑦 2 0 2 4 6

(b) 𝑦 = 3 𝑥 + 5

  • AThey have the same rate of change.
  • Ba
  • Cb

Q3:

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

Q4:

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)
  • BThis cannot be determined without more information.
  • C (b), (c), (a), (d)
  • D(b), (c), (d), (a)
  • E (a), (d), (c), (b)

Q5:

Yara 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

Q6:

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

(a)

(b) 𝑦 = 2 𝑥 9

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

Q7:

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

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

Q8:

A car manufacturer claims that the fuel consumption of one of their cars is 42 mi/gal (miles per gallon). Samar 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
  • Bless
  • Cmore

Q9:

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

  • Abeef
  • Bchicken

Q10:

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

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