P.1 Graphs and Models

Objectives  Sketch the graph of an equation.  Find the intercepts of a graph.  Test a graph for symmetry with respect to an axis and the origin.  Find the points of intersections of two graphs.  Interpret mathematical models for real-life data.

Graphing  One way to sketch a graph is to plot points as in example 1 on page 2.  You can get an inaccurate graph if you plot too few points.

Graphing Calculator  Zoom feature Zoom 6 (non-trig functions) Zoom 7 (trig functions)  Window settings

Intercepts  x-intercepts: where the graph crosses the x-axis (y=0)  y-intercepts: where the graph crosses the y-axis (x=0)  Calculator Calculate Value x=0 Calculate Zero

Example  Find x- and y-intercepts of the graph of

y-axis(x, y)  (-x, y) x-axis (x, y)  (x, -y) origin (x, y)  (-x, -y) Symmetry

Test for Symmetry  Replace x by –x  y-axis  Replace y by –y  x-axis  Replace x by –x and y by –y  origin

Shortcut IF POLYNOMIALS  All even powers of x  y-axis  All odd powers of x  origin  All even powers of y  x-axis

Example

Other examples y-axis origin neither

Example  We can use symmetry to help sketch a graph.  is symmetric to the x- axis. all even powers of y, or can replace y by –y  Can sketch upper part of graph by plotting points then reflect across the x-axis.

Graphing Calculator  How do you graph this on the calculator?  To graph on the calculator, you have to solve for y and then plot BOTH equations.

Points of Intersection  To find points of intersection you "solve a system of equations". substitution eliminiation

Example Find all points of intersection of the graphs of

Homework P.1: page 8 #1-4 all 5-11 odd odd odd odd (Don't sketch 37-53)