Math Problem Statement

graph of y=3^x

Solution

The graph of the exponential function y=3xy = 3^x is a curve that exhibits exponential growth as xx increases. Here's a description of its key features:

  1. Intercept: The graph passes through the point (0,1)(0, 1), because 30=13^0 = 1.
  2. Asymptote: The x-axis (y=0y = 0) is a horizontal asymptote. As xx decreases towards negative infinity, the graph gets closer to y=0y = 0, but never quite reaches it.
  3. Growth: For positive values of xx, the function grows rapidly as xx increases. For example:
    • When x=1x = 1, y=31=3y = 3^1 = 3
    • When x=2x = 2, y=32=9y = 3^2 = 9
    • As xx becomes large, yy 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