Stitz-Zeager_College_Algebra_e-book

# We need the following theorem theorem 67 change of

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Unformatted text preview: 10, e−1 , (0, 1), and (−10, e). Since none of these changes aﬀected the y values, the horizontal asymptote remains y = 0. Next, we see that the output from f is being multiplied by 90. This results in a vertical stretch by a factor of 90. We multiply the y -coordinates by 90 to obtain 10, 90e−1 , (0, 90), and (−10, 90e). We also multiply the y value of the horizontal asymptote y = 0 by 90, and it remains y = 0. Finally, we add 70 to all of the y -coordinates, which shifts the graph upwards to obtain 10, 90e−1 + 70 ≈ (10, 103.11), (0, 160), and (−10, 90e + 70) ≈ (−10, 314.64). Adding 70 to the horizontal asymptote shifts it upwards as well to y = 70. We connect these three points using the same shape in the same direction as in the graph of f and, last but not least, we restrict the domain to match the applied domain [0, ∞). The result is below. 7 We will discuss this in greater detail in Section 6.5. 334 Exponential and Logarithmic Functions y 180 y 7 160 6 140 5 120 4 100 3 80 2 60 H.A. y = 70 40 (0, 1) 20 −3 −2 −1 12 H....
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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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