Stitz-Zeager_College_Algebra_e-book

The unwritten2 property of logarithms is that if it

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Unformatted text preview: = 4 . Since the 5 4 base b = 5 is between 0 and 1, the graph of y = f (x) is decreasing. We plot the y -intercept (0, 1) and two other points, −1, 5 and 1, 4 , and label the horizontal asymptote y = 0. 4 5 4x To obtain V (x) = 25 5 , x ≥ 0, we multiply the output from f by 25, in other words, V (x) = 25f (x). In accordance with Theorem 1.5, this results in a vertical stretch by a factor of 25. We multiply all of the y values in the graph by 25 (including the y value of the horizontal asymptote) and obtain the points −1, 125 , (0, 25) and (1, 20). The horizontal 4 asymptote remains y = 0. Finally, we restrict the domain to [0, ∞) to fit with the applied domain given to us. We have the result below. y y 30 2 (0, 25) (0, 1) 20 15 10 −3 −2 −1 1 2 3 vertical scale by a factor of 25 H.A. y = 0 y = f (x) = 5 x 4x 5 −− − − − − − − − − − − − − − − − − − − −→ multiply each y -coordinate by 25 1 2 3456 H.A. y = 0 x y = V (x) = 25f (x), x ≥ 0 3. We see from the graph of V that its horizontal asymptote is y = 0. (We leave...
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