Lesson 1 Summary

 

In this lesson you explored exponential functions and how they can be used to describe growth or decay of quantities.

 

The characteristics of all exponential functions of the form y = cx, c > 0, c ≠ 1 are as follows:

• If c > 1, the function is increasing and is an exponential growth function.
• If 0 < c < 1, the function is decreasing and is an exponential decay function.
• The domain is {x|x ∈ R}.
• The range is {y|y > 0, y ∈ R}.
• There is no x-intercept.
• The y-intercept is 1.
• The horizontal asymptote is at y = 0.

When an exponential function is in the form y = a(c)b(x–h) + k, the parameters a, b, h and k correspond to the following transformations:

 

	Value > 0	Value < 0
a	vertical stretch of the graph by a factor of |a|	vertical stretch of the graph by a factor of |a|, and a reflection in the x-axis
b	horizontal stretch of the graph by a factor of	horizontal stretch of the graph by a factor of , and a reflection in the y-axis
h	translated to the right h units	translated to the left |h| units
k	translated up k units	translated down |k| units

 

Exponential functions can be used to model real-life applications of exponential growth or decay. In the next lesson you will explore how to solve exponential equations.