College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises - Page 409: 33

Answer

See the picture below
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Work Step by Step

By calculating a few pairs and connecting the dots on the graph with a smooth curve, we can graph both functions. A few pairs from the function $f(x)=2^x$ (with red colour): $f(0)=2^0=1$ $f(1)=2^1=2$ $f(2)=2^2=4$ $f(3)=2^3=8$ A few pairs from the function $f(x)=-2^{x+2}$ (with blue colour): $f(-1)=-2^{-1+2}=2^{1}=2$ $f(0)=-2^{0+2}=2^2=4$ $f(1)=-2^{1+2}=2^3=8$ $f(2)=-2^{2+2}=2^4=16$ As we can see the graph is translated 2 units left and then is reflected across the x-axis.
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