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P.1 Graphs and Models
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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.
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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.
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Graphing Calculator
3 2 25y x x
Zoom feature Zoom 6 (non-trig functions) Zoom 7 (trig functions)
Window settings
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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
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Example
Find x- and y-intercepts of the graph of
3 4 .y x x
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y-axis (x, y) (-x, y)
x-axis (x, y) (x, -y)
origin (x, y) (-x, -y)
Symmetry
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Test for Symmetry
Replace x by –x y-axis Replace y by –y x-axis Replace x by –x and y by –y origin
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Shortcut IF POLYNOMIALS
All even powers of x y-axis All odd powers of x origin
All even powers of y x-axis
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Example53 2y x x
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Other examples6 22 3 4y x x 5 32 3y x x 5 32 3 1y x x
y-axis
origin
neither
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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.
2 1x y
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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.
2 1x y
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Points of Intersection
To find points of intersection you "solve a system of equations". substitution eliminiation
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Example
Find all points of intersection of the graphs of 2 3 and 1.x y x y
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Homework
P.1: page 8#1-4 all5-11 odd
17-37 odd47-55 odd63-71 odd
(Don't sketch 37-53)