Math Problem Statement
graph of y=3^x
Solution
The graph of the exponential function is a curve that exhibits exponential growth as increases. Here's a description of its key features:
- Intercept: The graph passes through the point , because .
- Asymptote: The x-axis () is a horizontal asymptote. As decreases towards negative infinity, the graph gets closer to , but never quite reaches it.
- Growth: For positive values of , the function grows rapidly as increases. For example:
- When ,
- When ,
- As becomes large, becomes very large.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Graphing Functions
Formulas
y = 3^x
Theorems
Exponential Growth
Horizontal Asymptotes
Suitable Grade Level
Grades 9-12
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