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Exponential Functions Solutions

Using technology, think about the following questions, and then reveal the answers.

In an exponential equation, what happens when the value of h is changed? 

The graph is translated (slides) right or left.

In an exponential equation, what happens when the value of k is changed?
The graph is translated (slides) up or down.

Set h and k equal to zero before continuing. 

What is the end behavior when 0 < b < 1?
$\mathrm{As} x\to +\infty , f\left(x\right)\to 0, \mathrm{and} \mathrm{as} x\to –\infty , f\left(x\right)\to +\infty$

What is the end behavior when b > 1?
$\mathrm{As} x\to +\infty , g\left(x\right)\to +\infty , \mathrm{and} \mathrm{as} x\to –\infty , g\left(x\right)\to 0$

What does a negative a-value do to a graph?
The value of a reflects the graph over the x-axis.

What if a < 0 and 0 < b < 1?

What if a < 0 and b > 1?

What if a > 0 and 0 < b < 1?

What if a > 0 and b > 1?

Use of the Desmos Graphing Calculator and other Desmos Tools is used with permission from Desmos Studio, PBC.