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# Exponential Functions

From compound interest to bubonic plague, things that grow or spread really fast are often modeled by exponential functions. Learn about these powerful functions (pun intended?).

# Graphs of Exponential Functions

Which of the following could be the graph of $$y = - \frac{1}{a^x},$$ if $$a>1 ?$$

Let $$m$$ and $$n$$ be the maximum and minimum values, respectively, of $y=5 ^{1-x},$ where $$-1 \leq x \leq 1$$. What is the value of $$m-n$$?

The graph of $$y = 5^{-x + 3} + 7^{-x - 1} + 6$$ never goes below the line $$y = k.$$

What is the largest possible value of $$k$$ such that the statement above is true?

Let $$m$$ and $$n$$ be the maximum and minimum values, respectively, of $y=\left(\frac{1}{7}\right)^{-x^2+4x-5}$ in the interval $$2 \leq x \leq 3$$. What is the value of $$m+2n$$?

Shown above is the graph of $$y = f(x) ,$$ which is the reflection of $$y = 2^{2x+a} + b$$ in the $$y$$-axis. If the graph of $$y = f(x)$$ passes through $$(-1, 10)$$ and the equation of the graph's asymptote is $$y=2$$, what is $$a+b$$?

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