College Algebra Chapter 2 Functions and Graphs Section 2.3 Functions and Relations

1. Determine Whether a Relation is a Function 2. Apply Function Notation 3. Determine x- and y-intercepts of a Function Defined by y = f(x) 4. Determine Domain and Range of a Function 5. Interpret a Function Graphically

Determine Whether a Relation is a Function Definition of a Relation: A set of ordered pairs (x, y) is called a relation in x and y. The set of x values in the ordered pairs is called the domain of the relation. The set of y values in the ordered pairs is called the range of the relation.

Determine Whether a Relation is a Function Definition of a Function: Given a relation in x and y, we say that y is a function of x if for each value of x in the domain, there is exactly one value of y in the range.

Examples 1, 2: Determine if the relation defines y as a function of x

Example 3: Determine if the relation defines y as a function of x x y –2 6 

Examples 4, 5: Determine if the relation defines y as a function of x

Examples 6 – 8: Determine if the relation defines y as a function of x

Determine Whether a Relation is a Function Vertical Line Test: A graph defines y as a function of x if no vertical line intersects the graph in more than one point.

Examples 9 – 11: Determine if the graph defines y as a function of x 9. 10. 11.

1. Determine Whether a Relation is a Function 2. Apply Function Notation 3. Determine x- and y-intercepts of a Function Defined by y = f(x) 4. Determine Domain and Range of a Function 5. Interpret a Function Graphically

Example 12: Evaluate for the given values of x.

Example 13: Evaluate for the given values of x.

1. Determine Whether a Relation is a Function 2. Apply Function Notation 3. Determine x- and y-intercepts of a Function Defined by y = f(x) 4. Determine Domain and Range of a Function 5. Interpret a Function Graphically

Determine x- and y-intercepts of a Function Defined by y = f(x) Given a function defined by y = f (x): The x-intercepts are the real solutions to the equation f (x) = 0. The y-intercept is given by f (0).

Example 14: Find the x-and y-intercepts.

Example 15: Find the x-and y-intercepts.

Example 16: Find the x-and y-intercepts.

1. Determine Whether a Relation is a Function 2. Apply Function Notation 3. Determine x- and y-intercepts of a Function Defined by y = f(x) 4. Determine Domain and Range of a Function 5. Interpret a Function Graphically

Determine Domain and Range of a Function Given a relation defining y as a function of x, the domain is the set of x values in the function, and the range is the set of y values in the function.

Example 17: Determine the domain and range for the function Domain: _______________ Range: ________________

Example 18: Determine the domain and range for the function Domain: _______________ Range: ________________

Example 19: Determine the domain and range for the function Domain: _______________ Range: ________________

Example 20: Determine the domain and range for the function Domain: _______________ Range: ________________

1. Determine Whether a Relation is a Function 2. Apply Function Notation 3. Determine x- and y-intercepts of a Function Defined by y = f(x) 4. Determine Domain and Range of a Function 5. Interpret a Function Graphically

Example 21: Use the graph of to answer the following:

Example 21 continued: Use the graph of to answer the following:

Example 21 continued: Use the graph of to answer the following: Determine the x-intercept. Determine the y-intercept.

Example 21 continued: Use the graph of to answer the following: Determine the domain of f. Determine the range of f.