1. P.1 Graphs and Models Sketch the graph of an equation.
Find the intercepts of a graph.
Test a graph for symmetry wrt an axis and the origin.
Find the points of intersection of 2 graphs.
Interpret mathematical models for real-life data.

2. The Graph of an Equation
Solve 3x + y = 7.
This equation has many solutions.
The set of all solution points is the graph of the equation.

3. Sketch a Graph by Point Plotting
It is the most basic procedure --- but has a BIG shortfall: plotting too few points might NOT represent the actual graph.
(antidote: have a working knowledge of the graphs of different types of functions.)
Disadvantage of using technology

4. Intercepts of a graph These are solutions of the form (a,0) and (0,b).
To find the x-intercept a, set y to zero.
To find the y-intercept b, set x to zero.

5. Symmetry of a Graph
This is a good aid in graphing (besides point-plotting).
3 types:
a) y-axis symmetry: if (x, y) is a point in the graph, so is (-x, y).
b) x-axis symmetry: if (x,y) is a point in the graph, so is (x, -y).
c) origin: if (x,y) is a point in the graph, so is
(-x, -y).

6. Points of Intersection
A point of intersection of the graphs of 2 equations, also known as a system, is a point that satisfies both equations. Such a point is called a solution of the system.
To find points of intersection, either graph the 2 equations in the same plane, or solve the system algebraically by substitution.

7. Mathematical Models One of the end goals of mathematics: usefulness.
Aim for simplicity and accuracy: simple enough to be workable but accurate enough to produce meaningful results.