College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.3 - Exponential Functions - 6.3 Assess Your Understanding: 92

Answer

$f(x) = -e^x$

Work Step by Step

(1) In the exponential function, $\dfrac{f(x+1)}{f(x)} = a$ Using the points $(0, -1)$ and $(1, -e)$ and the formula in (1) above, $\dfrac{-e}{-1}=a \\e = a$ Thus, the tentative equation of the function is $f(x) = C \cdot e^x$. To find the value of $C$, use any point on the graph and substitute the x and y values of the point into the tentative equation above. Using the point (0,-1) gives: $f(x) = C \cdot e^x \\-1 = C \cdot e^0 \\-1= C \cdot 1 \\\frac{-1}{1} = C \\-1 = C$ Thus, the exponential function whose graph is given is $f(x) = -e^x$.
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