Five-Minute Check (over Lesson 1–5) Mathematical Practices Then/Now New Vocabulary Example 1: Representations of a Relation Example 2: Real-World Example: Independent and Dependent Variables Example 3: Analyze Graphs Lesson Menu

Mathematical Practices 1 Make sense of problems and persevere in solving them. Content Standards A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). MP

You defined appropriate quantities for descriptive modeling. Represent relations. Interpret graphs of relations. Then/Now

coordinate system relation mapping domain range independent variable coordinate plane x- and y-axes origin ordered pair x- and y-coordinates Vocabulary

Representations of a Relation A. Express {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column. Example 1

Graph Graph each ordered pair on a coordinate plane. Representations of a Relation Graph Graph each ordered pair on a coordinate plane. Example 1

Representations of a Relation Mapping List the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value. 4 –2 2 3 –1 –4 Domain Range Example 1

Representations of a Relation B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}. Answer: The domain for this relation is {4, –2, 2, 0}. The range is {3, –1, –4}. Example 1

A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping. A. C. B. D. Example 1

B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}. Example 1

Independent and Dependent Variables A. CLIMATE In warm climates, the average amount of electricity used rises as the daily average temperature increases and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function. Answer: Temperature is the independent variable, as it is unaffected by the amount of electricity used. Electricity usage is the dependent variable, as it is affected by the temperature. Example 2

Independent and Dependent Variables B. CALORIES The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function. Answer: The time is the independent variable. The number of calories burned is the dependent variable, as it is affected by the time. Example 2

C. x is the independent variable. y is the dependent variable. A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function. A. The number of new members is the independent variable. The dues is the dependent variable. B. Membership dues is the independent variable. The number of new members is the dependent variable. C. x is the independent variable. y is the dependent variable. D. Both variables are independent. Example 2

B. The area is independent, and the side length is dependent. B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function. A. The length of the side is independent, and the the area of the square is dependent. B. The area is independent, and the side length is dependent. C. Both variables are independent. D. Both variables are dependent. Example 2

The graph represents the temperature inside on a Analyze Graphs The graph represents the temperature inside on a winter day. Describe what happens in the graph. Sample answer: The temperature increases after the heat is turned on. Then the temperature fluctuates up and down because of the thermostat. Finally, the temperature drops when the heat is turned off. Example 3

The graph represents Macy’s speed as she swims laps in a pool The graph represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph. A. Macy is doing bobs. B. Macy’s speed increases as she crosses the length of the pool, but then decreases to zero when she turns around at the end of each lap. C. Macy is swimming at a constant speed. D. Macy’s speed continues to decrease. Example 3