Grade 8 Functions: Comparing Functions

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Ava has $20 and saves $8 each week. Ben's savings after x weeks are y = 12x + 25 dollars. How many more dollars per week does the faster saver save?

   1. Ava adds $8 every week, so her rate of change is 8 dollars per week (her $20 is just the starting value).
   2. Ben's rule y = 12x + 25 has slope 12, so he saves $12 per week.
   3. Compare the rates: 12 − 8 = 4.
   4. So the faster saver (Ben) saves 4 more dollars per week.

   Answer: 4

2. Example 2

   Function A is y = 8x + 1 and function B is y = 7x + 5. For what value of x do the two functions have the same value of y?

   1. Set the two rules equal: 8x + 1 = 7x + 5.
   2. Subtract 7x from both sides: x + 1 = 5.
   3. Subtract 1 from both sides: x = 5 − 1 = 4.
   4. Check: A gives 8 × 4 + 1 = 33 and B gives 7 × 4 + 5 = 33.
   5. So x = 4.

   Answer: 4

3. Example 3

   Function A's graph is a line through (0, −5) and (5, 30). Function B is y = 9x + 10. Which function has the greater slope? Give that slope.

   1. A: slope = change in y ÷ change in x = (30 − (−5)) ÷ (5 − 0) = 35 ÷ 5 = 7.
   2. B: y = 9x + 10 has slope m = 9.
   3. 9 is greater than 7, so function B grows faster.
   4. So the greater slope is 9.

   Answer: 9