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Interpreting Data and Determining Functions

This chapter focuses on interpreting data, determining functions, and calculating the range and domain of a function given a set. It covers topics such as ordered pairs, cartesian coordinate plane, quadrants, relation, domain, range, function, mapping, vertical line test, independent and dependent variables, functional notation, and examples.

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Interpreting Data and Determining Functions

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  1. Chapter 2 Section 1

  2. Objective Students will interpret the meaning of presented data and determine if the data represents a function. They will also be able to calculate the range and domain of a function given a domain and range set.

  3. Notes Ordered Pair - (2, 3) a relationship of data where 2 is the ordinate (horizonal) value and 3 is the abscissa (vertical) value. Cartesian Coordinate Plane - a horizontal and vertical set of axes which meet at the origin (0, 0). Quadrants - The four areas of the Cartesian Coordinate Plane formed by the intersecting axes. Relation - A set of ordered pairs. Domain - The set of all horizontal coordinates from the ordered pairs. Range - The set of all vertical coordinates from the ordered pairs.

  4. Notes Function - Each element of the domain is matched with exactly one element of the range. Mapping - Shows how each element of the domain is matched with each element of the range. One-To-One Funciton - Each element of the domain is paired with exactly one element of the range. Vertical Line Test - Passing a vertical line over a graph and the line only intersects the graph once at any one coordinate.

  5. Notes Independent Variable - Values which make up the Domain (horizontal coordinates). Dependent Variable - Values which make up the Range (vertical coordinates). Functional Notation - A Linear equation can be written as f(x) = 2x + 3 instead of y = 2x + 3 since y = f(x) “ f of x” is the functional notation for a linear function in math and f is just the name for the function.

  6. Example 1 State the domain and range or the relation shown in the graph. Is the relation a function? Domain: {-4, -3, 0, 1, 3} Range: {-2, 0, 1, 2, 3} Is the relation (9, 3), (9, -3), (4, 2), (4, -2) a function?

  7. Example 2 • The table shows the average fuel efficiency in miles per gallon for light trucks for several years. Graph this information and determine if it represents a function. The Relation of years to fuel efficiency is a function since no year has more than one value.

  8. Example 3 • 1.) Graph the relation represented by y = 3x – 1. • Find the domain and range. • Determine whether the relation is a function. The domain is the interval (-∞, +∞). The range is the interval (-∞, +∞). The Relation is a linear function since no x has more than one y value.

  9. Example 4 • 1.) Graph the relation represented by x = y2 + 1. • Find the domain and range. • Determine whether the relation is a function. The domain is {x | x ≥ 1}. The range is the interval (-∞, +∞) or all Real numbers. The relation is NOT a function since it does not pass the vertical line test.

  10. Example 5 • Given f(x) = x3 – 3 and h(x) = 0.3x2 -3x – 2.7, find the each value. • A.) f(-2) = B.) h(1.6)= C.) f(2t)= • Rewrite each problem and its solution as a relation. A.) f(-2) = -11 B.) h(1.6)= -6.732 C.) f(2t)= 8t3 - 3 A.) (-2, -11) B.) (1.6, -6.732) C.) (2t, 8t3 – 3)

  11. Assignment P. 60 17-22 all with an explanation, 24-34 even, 38-41 all, 46-52 even

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