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.

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.

Example of using some attributes Find the following attributes: Find f(0) and f(6)? Find f(2) and f(-2)? c) Is f(3) positive or negative? d) Is f(-1) positive or negative? e) For what value of x is f(x) = 0? f) For what value of x is f(x) < 0? g) What is the domain of f? h) What is the range of f? i) What are the x intercepts? j) What is the y intercept? Find the following attributes: k) How often does the line y = -1 intersect the graph. l) How often does the line x = 1 intersect the graph. m) For what value of x does f(x) = 3 n) For what value of x does f(x) = -2

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: D: [-π,π] R: [-1,1] X-intercepts:(0, -π), (0,0), (0,π) Y-intercept: (0,0) Symmetry: about the origin. Not a function Practice: D: (0,3) R: (-∞,2) X-intercepts: (1,0) Y-intercept: none Symmetry: none

Applying lessons together Answer the questions about the function: f(x) = -3x2 + 5x 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) = -2 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.