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Find the range of the exponential function. Write the range using interval notation.

Find the range of the exponential function. Write the range using interval notation.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Exponential Function Range Exercise** **Task:** Find the range of the exponential function. Write the range using interval notation. **Graph Explanation:** The graph shows an exponential function. The curve starts very close to the x-axis on the left and rises sharply as it moves to the right. The graph is positioned in the first quadrant, indicating that the y-values are positive as x increases. - **Axes:** - The horizontal axis is labeled "x," with increments from -10 to 10. - The vertical axis is labeled "y," with increments from -10 to 10. - **Curve Behavior:** - The curve approaches the x-axis as x becomes more negative, but never touches or crosses it, indicating the graph approaches zero but does not go below it. - The curve increases rapidly as x becomes more positive, moving upwards beyond y = 10. **Conclusion:** The exponential function shown on the graph has no maximum limit for y and never reaches or goes below y = 0. Therefore, the range of the function is all positive real numbers, expressed in interval notation as: \( (0, \infty) \).
Transcribed Image Text:**Exponential Function Range Exercise** **Task:** Find the range of the exponential function. Write the range using interval notation. **Graph Explanation:** The graph shows an exponential function. The curve starts very close to the x-axis on the left and rises sharply as it moves to the right. The graph is positioned in the first quadrant, indicating that the y-values are positive as x increases. - **Axes:** - The horizontal axis is labeled "x," with increments from -10 to 10. - The vertical axis is labeled "y," with increments from -10 to 10. - **Curve Behavior:** - The curve approaches the x-axis as x becomes more negative, but never touches or crosses it, indicating the graph approaches zero but does not go below it. - The curve increases rapidly as x becomes more positive, moving upwards beyond y = 10. **Conclusion:** The exponential function shown on the graph has no maximum limit for y and never reaches or goes below y = 0. Therefore, the range of the function is all positive real numbers, expressed in interval notation as: \( (0, \infty) \).
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