1. Lesson 1.2 – Page 17 Desk Standards: Reason quantitatively and use units to solve problems

2. Vocabulary Relation: is the mapping between a set of input values and a set of output values Domain: a set of input values Range: a set of output values Function: a relation between a given set of elements, such that for each element in the domain there exists exactly one element in the range. Vertical Line Test: a visual method used to determine whether a relation represented as a graph is a function. To apply the Vertical Line Test, consider all of the vertical lines that could be drawn on the graph of a relation. If any of the vertical lines intersect the graph of the relation at more than one point, then the relation is not a function. Discrete Graph: a graph of isolated points. Continuous Graph: a graph of points that are connected by a line or smooth curve on the graph. Continuous graphs have no breaks.

4. Problem 1 2) Compare your groupings with your classmates’ groupings. Create a list of the different graphical behaviors you noticed. always increasing from left to right always decreasing from left to right the graph both increases and decreases straight lines smooth curves discrete data values the graph has a maximum value the graph has a minimum value the graph is a function the graph is not a function the graph goes through the origin the graph forms a U shape the graph forms a V shape

5. Problem 2 1.Matthew grouped these graphs together. Why do you think he grouped these graphs in the same group? These graphs are made up of dots (discrete data)

6. Problem 2 2.Ashley grouped these together because they all show vertical symmetry. If she draws a vertical line through the middle of the graph the image is the same on both sides. Is her reasoning correct? Not totally – if graph V is extended there is symmetry What other graphs might show symmetry? B, E, I, Q, and U

7. Problem 2 3.Duane grouped these graphs together because each graph only goes through two quadrants Why is Duane’s reasoning incorrect? Even though it is not visible, Graph T continues into the first quadrant. Therefore, the graph goes through three quadrants. Each of the other graphs D, M, and P satisfy Duane’s reasoning. What other graphs only go into two quadrants? G, I, J, K, N, R, and U

8. Problem 2 4.Judy grouped these four graphs together but provided no rationale. What do you notice about the graphs? In each graph, for at least one value of x, there is more than one value of y. What rationale could Judy have provided? The graphs are not functions.

9. Problem 3 1.Analyze the four graphs Judy grouped together. Do you think that the graphs she grouped are functions? Explain how you determined your conclusion. No because there is more than on output per input. 2.Use the Vertical Line Test to sort the graphs in Problem 1 into two groups: functions and non-functions. Record your results by writing the letter of each graph in the appropriate column in the table shown. FunctionsNon-Functions A, B, C, D, F, G, H, I, K, L, M, O, P, Q, S, T, U, VE, J, N, R

10. Problem 3 3.Each graph in this set of functions has a domain that is either: the set of all real numbers, or the set of integers. For each graph, remember that the x-axis and the y-axis display values from -10 to 10 with an interval of 2 units. Label each function graph with the appropriate domain. All Real NumbersIntegers A, B, C, D, G, H, I, K, L, M, P, Q, S, T, U, and VF, O, R, and U

11. Talk the Talk Sketch a graph of a function. Explain how you know it is a function. For each value of x, there is exactly one value of y Sketch a graph that is not a function. Explain how it is not a function. For at least one value of x, there are two values of y.

12. Homework Complete the worksheet given out in class. It is due Monday August 30, 2015.