Attributes of functions in their graph Domain: the x values of a function. Range: the y values of a function. x-intercept: the point(s) where the graph crosses the x axis, the value of y must = 0. This is also called roots, zeros, and solutions. y-intercept: the point(s) where the graph crosses the y-axis, the value of x must = 0. Increasing: the interval at which a function is going up from left to right. Decreasing: the interval at which a function is going down from left to right. Constant: when a function is horizontal. Maximum: the greatest y value for the interval of the x values. Local maximum: the maximum over a part of the graph(certain interval) Minimum: the smallest y value for the interval of the x values. Local minimum: the minimum over a part of the graph(certain interval) Even: f(-x) = f(x) reflected across the y axis. Odd: f(-x) = -f(x) reflected across the origin.

Domain, Range, Intercepts, Symmetry Determine if the graph is a function. If it is then find the domain, range, x and y intercepts and any symmetry. Examples: Not a function Practice:

Where is the function increasing? From what x value to what x value? Copyright © 2013 Pearson Education, Inc. All rights reserved

Where is the function decreasing? From what x value to what x value?

Where is the function constant? Copyright © 2013 Pearson Education, Inc. All rights reserved

There is a local maximum when x = 1. (where, value) There is a local maximum when x = 1. The local maximum value is 2 Copyright © 2013 Pearson Education, Inc. All rights reserved

There is a local minimum when x = –1 and x = 3. The local minima values are 1 and 0. Copyright © 2013 Pearson Education, Inc. All rights reserved

(e) List the intervals on which f is increasing. (f) List the intervals on which f is decreasing.

N N E E V V E For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph. So for an odd function, for every point (x, y) on the graph, the point (-x, -y) is also on the graph.

Visual symmetry effect/ even odd function Visual symmetry effect/ even odd function. I am using a circle to show this attribute even though it is not a function. Even function/reflection Across the y axis. Odd function/reflection Across the origin.

Determine whether each graph given is an even function, an odd function, or a function that is neither even nor odd. Even function because it is symmetric with respect to the y-axis Neither even nor odd because no symmetry with respect to the y-axis or the origin. Odd function because it is symmetric with respect to the origin.

Copyright © 2013 Pearson Education, Inc. All rights reserved

Applying lessons together Answer the questions about the function: Pg. 77 # 23) f(x) = 2x2 – x – 1 Is the point (-1,2) on the graph of f? If x = -2 what is f(x)? What point is on the graph? If f(x) = -1 what is x? What point(s) are on the graph? What is the domain of f? List the x-intercepts, if any, of the graph of f. List the y-intercepts, it there is one, of the graph of f.

Practice: Pg. 89 # 21. a.) find intercepts b.) find domain and range c.) Where is the graph increasing, decreasing, constant d.) Even, odd, or neither

Domain, Range, Intercepts, Even, odd, neither, increasing decreasing and constant Find the the interval where it is increasing, decreasing, and constant, find any local maximums and minimums list their values and state whether it is even, odd or neither. Example: Increasing: (-1,1) and (3,∞) Decreasing: (-∞,1), and (1,3) Constant: never Local minimum at -1 & 3 values of 1 & 0 Local maximum at 1 value of 2 Neither even or odd no symmetry Practice Pg. 90 #31)

Practice: Pg. 90) #35 g(x) = -3x2 – 5