1. Types of Functions, Rates of Change Lesson 1.4

2. Constant Functions Consider the table of ordered pairs The dependent variable is the same It is constant The graph is a horizontal line Month123456 Rent Paid$735

3. Linear Function Can be represented by Where a and b are constants See Geogebra exampleexample

4. Slope and Y-Intercept 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

5. Family of Linear Functions Slope = Rate of Change y=3x + 5 Slope = m = 3 y-intercept = b = 5

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

7. Linear Functions Consider this set of ordered pairs If we plot the points and join them we see they lie in a line xy 05 18 211 314 417

8. Rate of Change Given function y = 3x + 5 xy 05 18 211 314 417 6 3

9. Rate of Change Try calculating for different pairs of (x, y) points You should discover that the rate of change is constant … in this case, 3 xy 05 18 211 314 417 Geogebra Demo

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

11. Family of Linear Functions Calculating slope with two ordered pairs (X 1, Y 1 ) (X 2, Y 2 ) Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

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

13. Rate of Change As before, determine the rate of change for different sets of ordered pairs xsqrt(x) 00.00 11.00 21.41 31.73 42.00 52.24 62.45 72.65

14. Rate of Change (NOT a constant) You should find that the rate of change is changing – NOT a constant. Contrast to the first function y = 3x + 5 Geogebra Demo

15. 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 Year1982198419861988199019921994 CD sales05.853150287408662 LP sales24420512572122.31.9

16. Warning Not all functions which appear linear will actually be linear!! Consider the set of ordered pairs Graph them Decide whether graph is linear Check slope for different pairs tP 067.38 169.13 270.93 372.77 474.67 576.61 678.60

17. Results Graph appears straight But … rate of change is not a constant tPslope 067.38 169.131.75 270.931.8 372.771.84 474.671.9 576.611.94 678.61.99

18. Assignment Lesson 1.4 Page 53 Exercises 1 – 65 EOO