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Unit 2.3

Unit 2.3. Represent Relations and Functions. Last year. You learned about relations, functions, domain, range, independent variables and dependent variables. Vocabulary. Relation – A mapping, or pairing, of input values with output values. Domain – The set of input values of a relation.

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Unit 2.3

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  1. Unit 2.3 Represent Relations and Functions

  2. Last year... • You learned about relations, functions, domain, range, independent variables and dependent variables

  3. Vocabulary • Relation – A mapping, or pairing, of input values with output values. • Domain – The set of input values of a relation. • Range – The set of output values of a relation. • Function – A relation for which each input value has exactly one output value. • Equation in two variables – An equation with an independent variable and a dependent variable, that depends on the value of the independent variable.

  4. Independent variable – The input variable of an equation. • Dependent variable – The output variable of an equation that depends on the value of the input variable. • Solution of an equation in two variables – An ordered pair (x, y) is a solution of an equation in two variables if substituting x and y into the equation produces a true statement. The graph of an equation in two variables is the set of all points (x, y) that represent solutions of the equation. • Linear function – Can be written in the form y = mx + b where m and b are constants, or in function notation as f(x) = mx + b. • One-to-one – A linear function is one-to-one if no two values in the domain have the same value in the range.

  5. Consider the relation given by the ordered pairs (1, 0), (0, -2), (-2, 3), and (3, 1). • Identify the domain and range. Domain: -2, 0, 1, 3 Range: -2, 0, 1, 3 • Represent the relation using a graph. • Use the vertical line test to tell whether the relation is a function. YES! • If the relation is a function, tell whether it is a one-to-one function. YES!

  6. Textbook • Page 35 # 1 - 6

  7. Which is a function?

  8. Textbook • Page 35 # 7 - 9

  9. Graph an equation in two variables. • y = -2x – 2 • Construct a table of values • Use slope-intercept • Use the x- and y-intercepts.

  10. Textbook • Page 35 # 11 – 13 • # 14, 15, 16, 18, 20, 22

  11. Tell whether the function is linear. Then evaluate the function when x = -3. • a. f(x) = 6x + 10 • b. g(x) = 2x² + 4x - 1

  12. Textbook • Page 36 # 23 – 28 • # 29 - 31

  13. Homework • Textbook Page 37 – 38 # 1 - 28

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