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Exploring Functions and Relations: From Theory to Practice

Dive into the world of relations, functions, domain, range, and variables. Learn to identify, graph, and evaluate equations, determining linearity and uniqueness. Practice with exercises and homework to reinforce your understanding.

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Exploring Functions and Relations: From Theory to Practice

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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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