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# 8.1 exponential growth

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### 8.1 exponential growth

1. 1. What are Exponential Functions? Exponential functions – functions that include the expression bx where b is a positive # other than 1. b is called the base.
2. 2. What’s the Shape? Let’s make a table to find the general shape. If we use f(x) = 2x as an example: x f(x) = 2x -3 -2 -1 0 1 2 3
3. 3. Asymptotes An asymptote is a line that a graph approaches (but does not touch) as you move away from the origin. For example: Our graph has a horizontal asymptote at y = 0.
4. 4. Graphing y = abx If a > 0 and b > 1, y = abx is an exponential growth function. For all y = abx , b > 1:  Graphs pass through (0, a) (a is the y-int)  x-axis is an asymptote  Domain: all real #s  Range: y > 0 if a > 0 y < 0 if a < 0
5. 5. To graph: Plot 2 points: (0, a) and (1, __)  Plug in 1 for x to fill the blank Connect with a smooth curve that:  Starts left of the origin, close to the x-axis  Moves up or down quickly to the right
6. 6. Examples Graph: