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Rates of Change

Rates of Change. Lesson 1.2. Which Is Best?. Which roller coaster would you rather ride? Why?. Today we will look at a mathematical explanation for why one is preferable to another. 6. 2. Rate of Change. Given function y = 3x + 5. •. •. •. •. Rate of Change.

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Rates of Change

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  1. Rates of Change Lesson 1.2

  2. Which Is Best? • Which roller coaster would you rather ride? • Why? Today we will look at a mathematical explanation for why one is preferable to another.

  3. 6 2 Rate of Change • Given function y = 3x + 5 • • • •

  4. Rate of Change • Try calculating for differentpairs of (x, y) points • You should discover that the rate of change is constant

  5. You may need to specify the beginning x value and the increment Rate of Change • Consider the function • Enter into Y= screen of calculator • View tables on calculator ( Y)

  6. Rate of Change • As before, determine therate of change fordifferent sets of orderedpairs

  7. Rate of Change • View spreadsheet which demonstrates results of the formula below.

  8. Rate of Change (NOT a constant) • You should find that the rate of change is changing – NOT a constant. • Contrast to thefirst functiony = 3x + 5

  9. Function Defined by a Table • Consider the two functions defined by the table • The independent variable is the year. • Predict whether or not the rate of change is constant • Determine the average rate of change for various pairs of (year, sales) values

  10. Increasing, Decreasing Functions • Note that for the CD sales, the rates of change were always positive • For the LP sales, the rates of change were always negative An increasing function A decreasing function

  11. A decreasing function An increasing function Increasing, Decreasing Functions

  12. Increasing, Decreasing Functions Given Q = f ( t ) • A function, f is an increasing function if the values of f increase as t increases • The average rate of change > 0 • A function, f is an decreasing function if the values of f decrease as t increases • The average rate of change < 0

  13. Use the STO> key Using TI to Find Rate Of Change • Define a function f(x)3*x + 5 -> f(x) • We want to define the functionand assign it to a function

  14. Using TI to Find Rate Of Change • Now call the function difquo( a, b ) using two different x values for a and b • For rate of change of a different function, redefine f(x)

  15. Assignment • Lesson 1.2 • Page 15 • Exercises • 3, 5, 7, 9, 11, 12, 13, 15, 21

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