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Comparing Function Rates
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Comparing Function Rates
Compare how quickly functions change. For each comparison, focus on the change in y for each 1-unit increase in x.
Understanding Rate of Change
1.Amara bikes 2 miles in 8 minutes. Madison bikes 2 miles in 12 minutes. Who is biking faster?
- Amara
- Madison
- They are biking at the same speed
2.For a function, what does its rate of change describe?
- How much the output changes for a given change in the input
- The starting value of the output only
- The greatest possible input
3.As x increases by 1, Function P's y-value increases by 4, while Function Q's y-value increases by 7. Which function has the greater rate of change?
- Function P
- Function Q
- Both have the same rate of change
Compare Rates in Different Forms
4.Function R is defined by y = 3x − 5. Function S's output increases by 5 whenever its input increases by 1. Which function has the greater rate of change?
- Function R
- Function S
- They have equal rates of change
5.Line A rises 2 units for every 1 unit it moves right. Line B rises 4 units for every 1 unit it moves right. Which line has the greater rate of change?
- Line A
- Line B
- They have equal rates of change
6.Complete the statement using Functions T and U. Function T is y = 6x + 1; Function U's output increases by 8 when its input increases by 1. Which function changes faster, and why?
Explain and Apply
7.A table for Function V has x-values 0, 1, 2, 3 and corresponding y-values 2, 7, 12, 17. What is Function V's rate of change?
8.Function W is given by y = 4x − 3. Compare its rate of change with Function V's rate from the table: x = 0, 1, 2, 3 and y = 2, 7, 12, 17. Which function changes faster? Explain with both rates.
9.Invent a real-world situation involving two quantities that change at different constant rates. State both rates and identify the faster rate.
10.In the equation y = mx + b, which variable gives the rate of change? Explain what it represents.
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