Graphing Functions - Notes

# Whose y value is the square of its x value is on this

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whose y-value is the square of its x-value is on this shape; any point whose y-value is not the square of its x-value is not on this shape. Hence, glancing at this shape gives us a complete visual picture of the function y = x 2 if we  know how to interpret it correctly . Graphing Functions Remember that every function specifies a relationship between two variables. When we graph a function, we put the independent variable  on the x-axis, and the dependent variable  on the y-axis. For instance, recall the function that describes Alice’s money as a function of her hours worked. Since Alice makes \$12/hour, her financial function is m ( t ) = 12t. We can graph it like this. This simple graph has a great deal to tell us about Alice’s job, if we read it correctly. The graph contains the point ( 3, 300 ) .What does that tell us? That after Alice has worked for three hours, she has made \$300. The graph goes through the origin (the point ( 0, 0 ) ). What does that tell us? That when she works 0 hours, Alice makes no money.

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Graphing Functions The graph exists only in the first quadrant. What does that tell us? On the mathematical level, it indicates the domain  of the function ( t 0) and the range  of the function ( m 0). In terms of the situation, it tells us that Alice cannot work negative hours or make negative money.
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