The graph of a function f is given. Use the graph to estimate the following. (Enter your answers using interval notation.) y WebAssign Plot (a) The domain and range of f. domain range (b) The intervals on whichfis increasing and on which f is decreasing. increasing decreasing

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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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,...
Question
### Understanding the Graph of a Function

The graph presented depicts a function \( f \). Use the graph to estimate the following characteristics of \( f \). Please enter your answers using interval notation.

#### Graph Description
The graph includes the following:
- A Cartesian plane with \( x \)- and \( y \)-axes.
- A red curve representing the function \( f \).
- A "WebAssign Plot" label indicating the platform used for plotting.

The curve appears to:
- Start from a point above the \( x \)-axis, ascend, and then descend crossing the \( x \)-axis.
- Continue to descend and then ascend again, forming a local minimum before crossing the \( x \)-axis again.

#### Questions

**(a) The domain and range of \( f \):**
- **Domain**: 
  - The set of all possible \( x \)-values (input values) for which the function is defined.
  - **Range**: 
  - The set of all possible \( y \)-values (output values) that the function can take.

**(b) The intervals on which \( f \) is increasing and on which \( f \) is decreasing:**
- **Increasing**:
  - The intervals in which the function \( f \) is rising as the \( x \) values increase.
- **Decreasing**:
  - The intervals in which the function \( f \) is falling as the \( x \) values increase.

Please refer to the visual representation on the graph to determine the appropriate intervals.
Transcribed Image Text:### Understanding the Graph of a Function The graph presented depicts a function \( f \). Use the graph to estimate the following characteristics of \( f \). Please enter your answers using interval notation. #### Graph Description The graph includes the following: - A Cartesian plane with \( x \)- and \( y \)-axes. - A red curve representing the function \( f \). - A "WebAssign Plot" label indicating the platform used for plotting. The curve appears to: - Start from a point above the \( x \)-axis, ascend, and then descend crossing the \( x \)-axis. - Continue to descend and then ascend again, forming a local minimum before crossing the \( x \)-axis again. #### Questions **(a) The domain and range of \( f \):** - **Domain**: - The set of all possible \( x \)-values (input values) for which the function is defined. - **Range**: - The set of all possible \( y \)-values (output values) that the function can take. **(b) The intervals on which \( f \) is increasing and on which \( f \) is decreasing:** - **Increasing**: - The intervals in which the function \( f \) is rising as the \( x \) values increase. - **Decreasing**: - The intervals in which the function \( f \) is falling as the \( x \) values increase. Please refer to the visual representation on the graph to determine the appropriate intervals.
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