Why can you be sure that the second number in the ordered pairs for this data is always greater than or equal to the first?

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1 Algebra II A Guided Notes Name 2-1 Guided Notes Period Relations and Functions Learning Matrix Goal #1: I can identify x & y intercepts in a graph or a set of ordered pairs. Learning Matrix Goal #2: I can use the definition of function to explain why there can be only one y- intercept. Learning Matrix Goal #3: I can identify increasing and decreasing intervals of a table or graph. Learning Matrix Goal #4: I can identify the domain and range of a relation. Learning Matrix Goal #5: I can explain how the domain and range of a function are represented in its graph. Learning Matrix Goal #6: I can evalute a function at a given value. Learning Matrix Goal #7: I can identify and explain the dependent and indepent variables. Learning Matrix Goal #8: I can describe and identify both functions and one-to-one functions. How do relations and functions apply to biology? Look at the table on p. 56 of your textbook. Now ask yourself this: What is the difference between average lifetime and maximum lifetime? Why can you be sure that the second number in the ordered pairs for this data is always greater than or equal to the first? Copy Coordinate Plane from page 56 (bottom right) Define vocabulary in your own words: Ordered pairs-

2 Cartesian coordinate plane- Quadrants- Relation- Domain- Function- Mapping- One-to-one function Complete the box p. 57 Concept Summary Functions Example 1 Domain and Range State the domain and range of the relation shown in the graph. Is the relation a function?

3 You can use the to determine whether a relation is a function Graph the following relation. State the domain and range. Is the relation a function? {(-4,0), (-3,1), (0,-2), (1,2), (3,3)} Explain why the set of order pairs {(9,3), (9,-3), (4,2), (3,-2)} is not a function Key Concept Vertical Line Test Words: Models: When two points on the graph of a relation are intersected by a vertical line, this means those two points have the same value but different values. Study Tip Vertical Line Test You can use a pencil to represent a vertical line. Slowly move the pencil to the right across the graph to see if it intersects the graph at more than one point.

4 Example 2 Vertical Line Test Geography The table shows the population of the state of Indiana over the last several decades. Graph this information and determine whether it represents a function. (Create a small coordinate plane from graph paper and attach it here). Year Population (millions) Notice also that each year is paired with only one population value. (So every value only has one value) Transportation The table shows the average fuel efficiency in miles per gallon for light trucks for several years. Graph this information and determine whether it represents a function. (Create a small coordinate plane from graph paper and attach it here). Year Fuel efficiency (mi/gal)

5 Example 3 Graph is a Line. (Paraphrase the following statements). a. Graph the relation represented by y = 2x + 1 Draw the table and the graph. b. Find the domain and range. x can be, so there is an of. Every is the x-coordinate of some point on the line. Also every, is the y-coordinate of some point on the line. So the domain and range are both. Symbolized in set notation by: Symbolized in interval notation by: c. Determine whether the relation is a function The graph passes the. Also, for each value, there is exactly one value, so the equation represents a. a. Graph the relation represented by y = 3x -1. b. Find the domain and range. Show in both set and interval notation.

6 c. Determine whether the relation is a function. Example 4 Graph is a Curve a. Graph the relation represented by x = - 2. Draw the tables and graph. In this case, it is easier to choose values and then find the corresponding values. Now sketch the graph by. b. Find the domain and range. Every is the coordinate of some point on the graph. So the range is. Symbolized in set notation by Symbolized in interval notation by Only real numbers greater than or equal to are coordinate points on the graph. So the domain is (symbolized in set notation) and (symbolized in interval notation) c. Determine whether the relation is a function.

7 a. Graph the relation represented by x = + 1. b. Find the domain and range. Show in both set and interval notation. c. Determine whether the relation is a function. Study Tip Reading Math Suppose you have a job that pays by the hour. Since you pay depends on the number of hours you work, you might say that your pay is a function of the number of hours you work. Your pay is the dependent variable, and the number of hours you work is the independent variable. (because how much you earn depends on how long you work) Define the following vocabulary: Independent variable- Dependent variable- Functional notation- Example 5 Evaluate a Function Given f (x) = and g (x) = 0.5, find each value. a. f (-3)

8 b. g (2.8) c. f (3z) Given f (x) = and h (x) = 0.3, find each value. a. f (-2) b. h(1.6) c. f(2t) Now you need to complete page 60 # 1-3, 17-22, odd, When assignment is complete, you should check your solutions (get them from the solutions folder). Mark correct problems with a star. Mark incorrect problems with an X and them make corrections on the problems that you had incorrect.

Chapter 11 GRAPHS OF LINEAR EQUATIONS

Chapter 11 GRAPHS OF LINEAR EQUATIONS 11.1 Graphs and Applications of Linear Equations Learning Objectives A Plot points associated with ordered pairs of numbers; determine the quadrant in which a point