Exponential Functions
1. Let \(\displaystyle{ f(x) = \left( \frac{1}{8} \right)^{x -
2} }\). Find the following.
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(a) \(\displaystyle{ f(1) }\)
(b) \(\displaystyle{ f(2) }\) (c) \(\displaystyle{ f\left(\frac{8}{3}\right) }\)
(d) Rewrite \(\displaystyle{ f(x) }\) as an exponential function
with base 2.
2. Solve the following:
(a) \(\displaystyle{ 8^{x + 3} = 16^{x - 1} }\)
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(b) \(\displaystyle{ \frac{8}{27} = \left(\frac{3}{2}\right)^x }\)
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(c) \(\displaystyle{ (\sqrt 2)^{2 - 3x} = \frac{1}{8} }\)
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(d) \(\displaystyle{ 3^{x^2 - 5x - 12} = 9 }\)
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(e) \(\displaystyle{ 5^{x^2 - 3x - 35} = \left( \frac{1}{5}
\right)^x }\) solution
3. The graph of \(\displaystyle{ y = 5^x }\) is shifted 2 units left
and 5 units up. What is the equation of the new graph?
Select the box for answer.
4. Starting with the graph of \(y=e^x\), use transformations to
sketch the graph of each of the following functions and state its
horizontal asymptote. (a) \(f(x)=e^{x-5}+1 \)
(b) \( g(x)=-e^{ x+2}-3\)
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