Describe the exponential graph.
Understand the Problem
The question is asking to describe the characteristics of an exponential graph, including its shape, intercepts, domain, and range.
Answer
Exponential, increasing. X-intercept: none, Y-intercept: 1. Domain: all real numbers, Range: y > 0. Horizontal asymptote: y=0. Continuous.
The general shape of the graph is exponential and the graph is increasing. From left to right, the graph is increasing. The x-intercept(s) are none and the y-intercept(s) are 1. The domain is all real numbers and the range is y > 0. There is a horizontal asymptote at y=0. The graph is continuous.
Answer for screen readers
The general shape of the graph is exponential and the graph is increasing. From left to right, the graph is increasing. The x-intercept(s) are none and the y-intercept(s) are 1. The domain is all real numbers and the range is y > 0. There is a horizontal asymptote at y=0. The graph is continuous.
More Information
Exponential graphs show rapid change and can model real-life growth processes like population growth or radioactive decay. They are characterized by a horizontal asymptote and a steady rate of increase or decrease.
Tips
A common mistake is assuming the range includes zero; remember the graph approaches but never reaches y=0.
Sources
- Exponential graphs | Lesson (article) - Khan Academy - khanacademy.org
- Exponential Graph - GCSE Maths - Steps, Examples & Worksheet - thirdspacelearning.com
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