1. 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.

2. 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.

3. 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

5. 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

6. 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.