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Section P.1 – Graphs and Models

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How to Graph xy Make a table to graph y = x 2 + 2 -5 -4 -3 -2 0 1 2 3 4 5 Use your knowledge of relations and functions to make sure you pick values of x that make a complete graph. 27 18 11 6 3 2 3 6 18 27 You do not need to plot every point, but make sure to get the complete graph. Only use a ruler if the relation is linear.

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Definitions x-interceptWhere the graph crosses the x-axis OR The value of x when y is 0. y-interceptWhere the graph crosses the y-axis OR The value of y when x is 0.

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Types of Symmetry With Respect to the… y-axisx-axisorigin Tests… Replacing x in the equation by –x yields an equivalent equation. Replacing y in the equation by –y yields an equivalent equation. Replacing x in the equation by –x and y by –y yields an equivalent equation.

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Example of Symmetry Test for symmetry in the equation. Check out the graph first. Test by Replacing x in the equation by –x. The equation is symmetric with respect to the y-axis. An equivalent equation.

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System of Equations Example Solve the following system of equation algebraically: Both equations equal y. Set them equal to each other.

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System of Equations Example Solve the following system of equation algebraically: No Solution. FALSE The two lines are parallel. They never intersect.

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System of Equations Example Solve the following system of equation algebraically:

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Determine if the following point is on the graph of the equation. 2x – y = 6; (2, 3) Step 1: Plug the given points into the given equation. 2(2) – (3)

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