Difference between revisions of "2003 AMC 12B Problems/Problem 9"
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Since <math>f</math> is a linear function with slope <math>m</math>, | Since <math>f</math> is a linear function with slope <math>m</math>, | ||
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<cmath>f(12) - f(2) = m \Delta x = 3(12 - 2) = 30 \Rightarrow \text (D)</cmath> | <cmath>f(12) - f(2) = m \Delta x = 3(12 - 2) = 30 \Rightarrow \text (D)</cmath> | ||
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+ | ==Solution 2== | ||
+ | Since <math>f</math> is linear, we can easily guess and check to confirm that <math>f(x)=3x</math>. Indeed, <math>f(6)-f(2)=3(6-2)=12</math>. So, we have <math>f(12)-f(2)=3(12-2)=30 \Rightarrow \text (D).</math> | ||
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+ | Solution by franzliszt | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2003|ab=B|num-b=8|num-a=10}} | {{AMC12 box|year=2003|ab=B|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 18:05, 7 July 2020
Contents
Problem
Let be a linear function for which What is
Solution 1
Since is a linear function with slope ,
Solution 2
Since is linear, we can easily guess and check to confirm that . Indeed, . So, we have
Solution by franzliszt
See Also
2003 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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