Identify properties of functions represented in tables, equations, and verbal descriptions. Evaluate functions.
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Lessons 3 and 4 focus on functions represented in tables, equations, and verbal descriptions. In Lesson 3, students analyze these representations to make sense of the relationships between the quantities (MP.2). They use their understanding of unit rate and constant of proportionality to determine the rate of change between quantities. They consider what a starting or initial value means in context of a situation, and how to determine these values from a table or equation.
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The function formula below shows the relationship between temperature in degrees Fahrenheit and degrees Celsius. °F is a function of °C.
$${F=\frac{9}{5}C+32}$$
Determine the rate of change in each situation. Then describe the relationship using function language (for example, ____ is a function of ____ because _____.)
Amount of watermelon in pounds, x | 0 | 0.25 | 0.5 | 1.5 | 2 | 3 | 5 |
Cost of watermelon y | $0 | $0.35 | $0.70 | $2.10 | $2.80 | $4.20 | $7.00 |
$${d=25t}$$, where $$d$$ is distance in miles and $$t$$ is time in hours
Giovanni can decorate $$2$$ cakes, $$c$$, every $$5$$ hours, $$h$$.
Determine the starting or initial output value in each situation.
Miles traveled in cab, x | 0 | 1 | 3 | 4 |
Cost of cab ride, y | $2.50 | $4.75 | $9.25 | $11.50 |
Miles traveled in cab, x | 1 | 2 | 4 | 5 |
Cost of cab ride, y | $4.50 | $7.00 | $12.00 | $14.50 |
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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The formula below represents simple interest, $$I$$, as a function of the principle amount, $$P$$, the simple interest rate, $$R$$, and the time of the investment, $$T$$.
$$I=PRT$$
Determine the principle amount, $$P$$, when $${$8.50}$$ of interest has been earned after $${1.25}$$ years with an annual rate of $$2$$%.
The table below shows the number of miles Alan biked over time. Alan biked at a constant speed. Find the rate of change.
Time in hours, x | 0 | 0.5 | 2 | 4 | 4.5 | 6 |
Miles biked, y | 0 | 7.5 | 30 | 60 | 67.5 | 90 |
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