College Algebra (Abridged)

The input for the function is known as the independent variable while the output derived from this function is known as dependent variable. We can plot a function on a graph. For instance, take the example: ( ) = 3 2 – 4 In this function, is the independent variable while the expression 3 2 – 4 represents a dependent variable. In order to plot this function, find the value of this output for different values of . − ( ) ( , ) − 2 3( − 2) 2 – 4 = 8 8 ( − 2,8) − 1 3( − 1) 2 – 4 = − 1 − 1 ( − 1, − 1) 0 3(0) 2 – 4 = − 4 − 4 (0, − 4) 1 3(1) 2 – 4 = − 1 − 1 (1, − 1) 2 3(2) 2 – 4 = 8 8 (2,8) Plotting these points on the graph and joining them, we get the following graph:

Similarly, we can graph any equation with number of leading terms. However, there are some translation rules for graphing functions: ( ) + is ( ) shifted upward units ( )– is ( ) shifted downward units ( + ) is ( ) shifted left units ( – ) is ( ) shifted right units – ( ) is ( ) reflected over the -axis f(–x) is the mirror of ( )

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