Algebra 1 ~ Chapter 4.1

1. Algebra 1 ~ Chapter 4.1 • The Coordinate Plane

2. 4-1: The Coordinate Plane -Where we graph points. -A grid created by two intersecting lines we call Axes. -Each axis is like a number line. -One horizontal line. -One vertical line. -These Axes divide the coordinate plane into 4 quadrants. Y-Axis (Vertical Line) II I X-Axis (Horizontal Line) III IV

3. Points Points are called Ordered Pairs. Ordered Pairs are written in the form of (x,y) (x-coordinate, y-coordinate) (Direction along the x-axis, Direction along the y-axis) Y X

4. Origin (0,0) Origin: (0 along the x-axis,0 along the y-axis)

5. Signs of Points Ordered Pairs have unique signs depending upon the quadrant they appear in… Quadrant I Quadrant II Quadrant III Quadrant IV (– ,+) (+,+) (–, –) (+, –)

6. Find the Ordered Pair:Fill In the Table 1 2 (1,2) I .A 2 -1 (2, –1) IV –1 –2 III (–1, –2) .B .C

7. Graphing Ordered Pairs How to draw a point on the coordinate plane that corresponds to that ordered pair. 1)Start at the origin 2)Move x units horizontally first 3)Then move y units vertically (x,y)

8. Practice Graphing Points Graph: A: (2, 3) B: (0, –3) C: (–2, 0) D: (–1, –2) E: (4, –1) F: (–3, 3) .F .A .D .B .C .E

9. Chapter 4.3 • Relations

10. In Chapter 1, we learned that a set of ordered pairs (coordinates) is called a relation. A relation can be represented by a set of ordered pairs, a table, a graph or a mapping diagram. A mapping diagram will illustrate how each element of the domain (the x’s) is paired with an element in the range (the y’s).

11. Representing Relations

12. Table x y 2 3 4 7 6 8 Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Write all x-values under “x” and all y-values under “y”.

13. Example 1 Continued Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Graph Use the x- and y-values to plot the ordered pairs.

14. 2 3 4 7 6 8 Example 1 Continued Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Mapping Diagram y x Write all x-values under “x” and all y-values under “y”. Draw an arrow from each x-value to its corresponding y-value.

15. Remember that the domain of a relation is the set of first coordinates (or x-values) of the ordered pairs. The rangeof a relation is the set of second coordinates (or y-values) of the ordered pairs.

16. Example 2 – Use the mapping diagram below to identify the domain and range. Domain {-3, -2, -1, 0, 3} Range {-3, -2, 2, 4} Notice that 2 of the 5 coordinates have a y-value of 4, but we only list the 4 once on the “range” list. Also, notice that we listed the numbers in order from least to greatest.

17. 6 –4 5 –1 2 0 1 Example 3 – Write the four ordered pairs represented in the mapping diagram. {(6, -1), (5, 0), (2, -4), (1, 0)}

18. x y 1 1 4 4 8 1 Example 4 – Identify the ordered pairs represented by the table. {(1, 1), (4, 4), (8, 1)}

19. Page 206 ~ Bald Eagles Example The data is given in a table and then we can use that information to make a graph. The x-values (domain) are years. The y-values (range) are the # of eagles.

20. Inverse Relations • The inverse of any relation is obtained by switching the coordinates in each ordered pair. • For example, ordered pair (a, b) has the inverse ordered pair (b, a).

21. Relation - Inverse Relation (2, 5) (-3, 2) (6, 7) (5, -1) Inverse (5, 2) (2, -3) (7, 6) (-1, 5) Notice that the domain of a relation becomes the range of the inverse and the range of a relation becomes the domain of the inverse.

22. Lesson Review 1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram.

23. Assignment • Skills Worksheet 4-1 / 4-3 (Front & Back)