For example we stated earlier that 9x 3 x with the

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Unformatted text preview: and to make good use of this fact, we set Bx + H = a and solve. We first subtract the H (causing the horizontal shift) and then divide by B . If B 100 Relations and Functions 1 is a positive number, this induces only a horizontal scaling by a factor of B . If B < 0, then we have a factor of −1 in play, and dividing by it induces a reflection about the y -axis. So we have x = a−H as the input to g which corresponds to the input x = a to f . We now evaluate B g a−H = Af B · a−H + H + K = Af (a) + K = Ab + K . We notice that the output from f is B B first multiplied by A. As with the constant B , if A > 0, this induces only a vertical scaling. If A < 0, then the −1 induces a reflection across the x-axis. Finally, we add K to the result, which is our vertical shift. A less precise, but more intuitive way to paraphrase Theorem 1.7 is to think of the quantity Bx + H is the ‘inside’ of the function f . What’s happening inside f affects the inputs or x-coordinate...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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