2. Chapter 01 – Section 08 A Preview of Graphs and Functions

3. © William James Calhoun To interpret graphs in real-world settings, and to sketch graphs for given functions. This can also be shown in a graph. The dollar value of a car begins to decrease immediately after it leaves the lot. This is called depreciation. depreciation = original cost of car - value of car when sold The following table shows how a typical $15,000 car depreciates.

4. © William James Calhoun Graphing Terms: function - a relationship between input and output the output depends on the input and there is only one output for every input vertical axis - the upward axis represents current car value from the sample graph horizontal axis - the sideways axis represents age of car from the sample graph ordered pair - a pair of numbers used to locate points on a graph examples from the sample graph are: (2, 8), (1, 11), and (3, 6) in ordered pairs, the horizontal # always comes first origin - the point on a graph where all values are zero Generally, this is the point (0, 0).

5. © William James Calhoun Horizontal Axis Vertical Axis Origin Function - the equation being graphed by the purple line (1, 6) (2, 1) (3, 2) (5, 3) Ordered Pairs (4, 8) Here is a labeled diagram of a graph.

6. © William James Calhoun EXAMPLE 1α: Shim owns a farm market. The amount a customer pays for sweet corn depends on the number of ears that are purchased. Shim sells a dozen ears of corn for $3.00. a. Make a table showing the price of various purchases of sweet corn. b. Write four ordered pairs that represent the number of ears of corn and the price of the corn. c. Describe a set of axes that could be used to graph the number of ears of corn and the price of the corn. d. Draw a graph that shows the relationship between the number of ears of corn and the price. e. As you read the graph from left to right, describe the trend you see. Explain. This example will spread across the next few slides.

7. © William James Calhoun a. Make a table showing the price of various purchases of sweet corn. Sample amounts chosen were: 0.5, 1, 1.5, and 2 dozen b. Write four ordered pairs that represent the number of ears of corn and the price of the corn. Get this information from the chart. ordered pair = (ears of corn, price) (6, 1.5), (12, 3), (18, 4.5), (24, 6) c. Describe a set of axes that could be used to graph the number of ears of corn and the price of the corn. Let the horizontal axis represent the number of ears of corn, and let the vertical axis represent the price of the corn.

8. © William James Calhoun d. Draw a graph that shows the relationship between the number of ears of corn and the price. First, draw the axes. Second, choose the scale of the axes. Third, draw the scale. Finally, plot the points. First, draw the axes.Second, choose the scale of the axes. 6 3 4812162024 Third, draw the scale. Price only goes up to $6.00, so from $0 to $6. Number of Ears ranges from 0 to 24. This sets the max & min values. 0 Number of Ears Price (in $) Finally, plot the points. (6, 1.5) (12, 3) (18, 4.5) (24, 6) e. As you read the graph from left to right, describe the trend you see. Explain. The graph goes upward, because the price increases as the number of ears increases. The price is a function of the number of ears purchased.

9. © William James Calhoun As the number of ears of corn changed, the price a customer paid changed. This is an example of two types of variables: those that lead the change; and those that change due to the leaders changing. independent variable - a variable that changes because something such as humans or time change it usually graphed on the horizontal axis will generally be x when we graph dependent variable - a variable that changes because the independent variable was changed usually graphed on the vertical axis will generally be y when we graph

10. © William James Calhoun EXAMPLE 1α: For a certain time, Lucinda jogs up a hill at a steady speed. Then she runs down the hill and picks up her speed. a. What happens to her speed when Lucinda jogs at a steady pace? When Lucinda runs down the hill? The speed remains the same when her jogging pace is steady. The speed increases when she runs downhill. b. Identify the independent and dependent quantities. Time is the independent quantity, and speed is the dependent quantity. c. Match the graph to the situation of Lucinda jogging. Which one fits best with the information we are given? Graph 1 Speed Time Graph 3 Speed Time Graph 2 Speed Time This is it because it shows a steady speed for the uphill and an increased speed when going downhill.

11. © William James Calhoun A few last terms: relation - a set of ordered pairs domain - the set of first numbers from a set of ordered pairs range - the set of second numbers from a set of ordered pairs The following is a relation. The domain is in blue and the range is in red. relation -> {(1, 2), (3, 5), (8, 4), (6, 2), (3, 1), (7, 4)} domain -> {1, 3, 8, 6, 3, 7} range -> {2, 5, 4, 2, 1, 4} {1, 3, 6, 7, 8} To “spell” it right, {1, 2, 4, 5} in order & no repeats.