Lesson 4 34 6 Relations and Functions Pages

Lesson 4 -3&4 -6 Relations and Functions Pages 241 -246

Video • Domain & Range

A function is a mathematical process that uniquely relates one variable (input) to another variable (output) Input Domain Independent X Function f(x) Output Range Dependent Y

A relation is a set of ordered pairs. The (age, height) ordered pairs below form a relation.

The domain of a relation is the set of first coordinates of the ordered pairs. The range is the set of second coordinates.

Find the domain and range of the ordered pairs in the chart. List the values in order. Do not repeat values.

Find the domain and range of the relation represented by the data in the table.

A function is a relation that assigns exactly one value in the range to each value in the domain. One way you can tell whether a relation is a function is to analyze the graph using the vertical line test. If any vertical line passes through more than one point of the graph,

Use the vertical line test to determine whether each relation is a function. Graph the points first. a. {(4, 2), (1, 2), (0, 1), (-2, 2)} b. {(0, 2), (1, -1), (0, -3), (2, 1)}

• Use a mapping diagram to determine whether each relation is a function. a. {(3, -2), (8, 1), (9, 2), (3, 3), (-4, 0)} b. {(6. 5, 0), (7, -1), (6, 2), (2, 6), (5, -1)}

A function rule is an equation that describes a function. You can think of a function rule as an input-output machine.

If you know the input values, you can use a function rule to find the output values.

Another way to write the function y = 3 x + 4 is f(x) = 3 x + 4. A function is in function notation when you use f(x) instead of y. The notations g(x) and h(x) also indicate functions of x.

Evaluate each function rule for x = 2 a. y = 2 x + 1 b. f(x) = x² - 4 c. g(x) = -x + 2