Functions (Section 1-2) Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range.

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Function: a relationship between two variables such that to each value of the independent variable there corresponds exactly one value of the dependent variable.  y is the dependent variable  x is the independent variable Domain: is the set of all values (input or x-values) of the independent variable for which the function is defined.  If x is in the domain of f, f is said to be defined at x.  If x is not in the domain of f, f is said to be undefined at x. Range: is the set of all values (output or y-values) assumed by the dependent variable (that is, the set of all function values.) Implied Domain: If f is defined by an algebraic expression and the domain is not specified the implied domain consists of all real numbers for which the expression is defined.

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Section 1.3, Figure 1.19, Illustration of Domain and Range [ ] = closed ( ) = open, arrows

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range.

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Does the relation describe a function? Example 1 a) b)

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Decide whether the relation represents y as a function of x. Explain your reasoning. Example 2 Input, x01210 Output, y

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Which sets of ordered pairs represent functions from A to B? Example 3 A = {1, 2, 3} and B={4, 5, 6, 7} a){(1, 4), (3, 6), (3, 7), (2, 7) b){(1, 4), (2, 6), (3, 7)} c){(5, 1), (4, 1), (6, 3), (7, 2)} d){(3, 1), (2, 4), (1, 7)}

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Determine whether the equation represents y as a function of x. Example 4

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Determine whether the equation represents y as a function of x. Example 5

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Evaluating a function Plug exactly what is inside the parentheses in where the variable was originally.

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Evaluate the function at each specified value of the independent variable and simplify. Example 6 g(y) = 7 – 3y a)g(0) b) c) g(s+2)

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Evaluate the function at each specified value of the independent variable and simplify. Example 7 a)g(2) b)g(t) c)g(x+2) g(x) = -x 2 + 4x + 1

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find all real values of x such that f(x) = 0. Example 8 f(x) = 5x + 1

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find all real values of x such that f(x) = 0. Example 9

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find the value(s) of x for which f(x) = g(x). Example 10 f(x) = x 2 + 2x + 1 g(x) = 7x - 5

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find the domain of each function. Example 11 f{(-3,0), (-1,4), (0,2), (2,2), (4,1)} Example 12 g(x) = 1 – 2x 2 Example 13 Example 14 Volume of a sphere: Example 15

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Use a graphing utility to find the domain and range. Example 16

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find the difference quotient and simplify your answer. Example 17

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range. Find the difference quotient and simplify your answer.

Essential Question: How do you find the domain and range of a function? Students will write a description of domain and range.