Functions and Graphing Identify the domain and range of a relation and determine if the relation is a function. 2.Find the value of a function. 3.Graph functions. Graphs of Quadratic Equations and Functions Graph quadratic equations in the form y = ax 2 + bx + c. 2.Graph quadratic functions.

Relation: Domain: Range: Function: A set of ordered pairs. The set of all input values (x-values) for a relation. The set of all output values (y-values) for a relation. A relation in which every value in the domain is paired with exactly one value in the range.

Identify the domain and range and tell if it is a function. {(−4, −1), (−2, 1), (0, 0), (2, −1), (4, 2)} Domain: Range: Function: {-4, -2, 0, 2, 4} {-1, 1, 0, 2} Yes

Identify the domain and range and tell if it is a function. Domain: Range: Function: (-∞, ∞) [-2, ∞) Yes

Find f(-3) for

Graph:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Quadratic equation in two variables: An equation that can be written in the form y = ax 2 + bx + c, where a, b, and c are real numbers and a  0. Shape: Parabola Axis of symmetry: A line that divides a graph into two symmetrical halves. Vertex: The lowest point on a parabola that opens up or the highest point on a parabola that opens down. Function: vertex (0, 0) axis of symmetry x = 0 (y-axis) Yes

Graph. f(x) = 2x 2 xf(x)f(x) 22 1

Graph. xf(x)f(x) 22 1

Opening of a Parabola For y = ax 2 + bx + c a > 0: opens upward a < 0, opens downward

Graph. f(x) = | x | xf(x)f(x) 22 1

Graph. f(x) = | x – 1 | + 3 xf(x)f(x) 22 1

Graph. xf(x)f(x)

When an equation in one variable is solved the answer is a point on a line. Library of Functions

Slide Copyright © 2011 Pearson Education, Inc. Which could be the graph of a)b) c)d)

Slide Copyright © 2011 Pearson Education, Inc. Which could be the graph of a)b) c)d)

Slide Copyright © 2011 Pearson Education, Inc. Which could be the graph of a)b) c)d)

Slide Copyright © 2011 Pearson Education, Inc. Which could be the graph of a)b) c)d)