Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 87


$f(x) = -6^x$

Work Step by Step

The exponential function has the form: $\dfrac{f(x+1)}{f(x)} = a(1)$ We will use the points $(1, -6)$ and $(2, -36)$ in equation (1) to obtain: $\dfrac{-36}{-6}=a \implies a=6$ Thus, we can write the equation of the function as: $f(x) = C \cdot 6^x$. In order to compute the value of $C$, we will apply the point $x=1; y=f(x)=-6$ as follows: $-6 = C \times 6^{(1)} \\C= \dfrac{-6}{6} \\ C=-1$ Therefore, the required exponential function is of the form: $f(x) = -6^x$
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