Write, graph, and evaluate exponential decay functions.
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Compare and contrast functions $${{f(x)}}$$ and $${{g(x)}}$$ by answering the questions below.
$${{f(x)}}=\left({1\over2}\right)^x$$
$${{g(x)}}=(2)^x$$
a. What happens to the values of $${{f(x)}}$$ and $${{g(x)}}$$ as $$x$$ increases?
b. What are the domains of $${{f(x)}}$$ and $${{g(x)}}$$?
c. What are the ranges of $${{f(x)}}$$ and $${{g(x)}}$$?
d. Create a table of values for each function and use them to sketch a graph of each function.
Consider the exponential graph below.
Sketch a graph of each function shown below.
$${f(x)=2(3)^{-x}}$$
$${g(x)=\left(1\over2\right)^x-3}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Graph the exponential function $${f(x)=-\left({1\over2}\right)^x}$$.
Write the equation for the graph shown below.