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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?).

Graphing 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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