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Types of Functions, Rates of Change

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Types of Functions, Rates of Change

Lesson 1.4

- Consider the table of ordered pairs
- The dependent variable is the same
- It is constant

- The graph is a horizontal line

- Can be represented by
- Where a and b are constants

- See Geogebra example

- Considering y = m * x + b
- The b is the y-intercept
- Where on the y-axis, the line intersects

- On your calculator
- Go to Y= screen
- Enter at Y1 (2/3) * x + 5
- Predict what the graph will look like before you specify F2, 6 for standard zoom

- Slope = Rate of Change

y=3x + 5

- Slope = m = 3
- y-intercept = b = 5

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- The function y = (2/3) * x + 5
- Slope = 2/3 (up to the right)
- Y-intercept = 5

- Consider this set ofordered pairs
- If we plot the pointsand join them wesee they lie in aline

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3

- Given function y = 3x + 5

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- Try calculating for differentpairs of (x, y) points
- You should discover that the rate of change is constant … in this case, 3

GeogebraDemo

- When slope =
- Try y = -7x – 3(predict the results before you graph)

- Calculating slope with two ordered pairs

(X2, Y2)

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(X1, Y1)

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Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

You may need to specify the beginning x value and the increment

- Consider the function
- Enter into Y= screen of calculator
- View tables on calculator (♦ Y)

- As before, determine therate of change fordifferent sets of orderedpairs

- You should find that the rate of change is changing – NOT a constant.
- Contrast to thefirst functiony = 3x + 5

GeogebraDemo

- 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

- Not all functions which appear linear will actually be linear!!
- Consider the set of ordered pairs
- Graph them
- Decide whether graphis linear
- Check slope for differentpairs

- Graph appearsstraight
- But …rate of change is not a constant

- Lesson 1.4
- Page 53
- Exercises 1 – 65 EOO