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What is the domain of the function shown in the graph below? -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 X

What is the domain of the function shown in the graph below? -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 X

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Answer Section** **Attempt 1 out of 2** **Answer Type:** Dropdown menu reads "Interval" **Interval:** Text box for input. **Symbols and Buttons:** - **Bracket Options:** - \[ \] : Closed interval brackets - \[ \) : Half-open interval, closed on the left - \( \] : Half-open interval, closed on the right - \( \) : Open interval brackets - **Infinity Symbols:** - \( -\infty \) : Negative infinity symbol - \( \infty \) : Positive infinity symbol - **Operators and Additional Symbols:** - \( \cup \) : Union symbol - \( \leq \) : Less than or equal to - \( \geq \) : Greater than or equal to - "or" button, allowing inclusion of alternative options **Submit Button:** Blue button labeled "Submit Answer" for submitting responses.
Transcribed Image Text:**Answer Section** **Attempt 1 out of 2** **Answer Type:** Dropdown menu reads "Interval" **Interval:** Text box for input. **Symbols and Buttons:** - **Bracket Options:** - \[ \] : Closed interval brackets - \[ \) : Half-open interval, closed on the left - \( \] : Half-open interval, closed on the right - \( \) : Open interval brackets - **Infinity Symbols:** - \( -\infty \) : Negative infinity symbol - \( \infty \) : Positive infinity symbol - **Operators and Additional Symbols:** - \( \cup \) : Union symbol - \( \leq \) : Less than or equal to - \( \geq \) : Greater than or equal to - "or" button, allowing inclusion of alternative options **Submit Button:** Blue button labeled "Submit Answer" for submitting responses.
**Understanding the Domain of a Function** When analyzing the graph of a function, the domain refers to the set of all possible input values (x-values) for which the function is defined. ### Graph Description: - **Axes**: This graph shows the x-axis (horizontal) and y-axis (vertical) extending from -10 to 10. - **Function Behavior**: The function is represented by a curve with two distinct parts: - To the left of x = 2, the curve approaches but never touches the line x = 2 from the left. It is somewhat horizontal and stretches along the negative side of the x-axis. - To the right of x = 2, the curve starts from below and rises steeply, approaching x = 2 as it moves leftward. ### Analysis of the Domain: - **Exclusion Point**: The function is undefined at x = 2, which is evident from the way the curve approaches the line x = 2 but never crosses it. This indicates a vertical asymptote. - **Domain**: Considering these observations, the domain of the function is all real numbers except x = 2, which can be expressed in interval notation as: - Domain: \( (-\infty, 2) \cup (2, \infty) \) This graphical representation is vital for understanding restrictions on inputs that are critical for ensuring the function operates correctly.
Transcribed Image Text:**Understanding the Domain of a Function** When analyzing the graph of a function, the domain refers to the set of all possible input values (x-values) for which the function is defined. ### Graph Description: - **Axes**: This graph shows the x-axis (horizontal) and y-axis (vertical) extending from -10 to 10. - **Function Behavior**: The function is represented by a curve with two distinct parts: - To the left of x = 2, the curve approaches but never touches the line x = 2 from the left. It is somewhat horizontal and stretches along the negative side of the x-axis. - To the right of x = 2, the curve starts from below and rises steeply, approaching x = 2 as it moves leftward. ### Analysis of the Domain: - **Exclusion Point**: The function is undefined at x = 2, which is evident from the way the curve approaches the line x = 2 but never crosses it. This indicates a vertical asymptote. - **Domain**: Considering these observations, the domain of the function is all real numbers except x = 2, which can be expressed in interval notation as: - Domain: \( (-\infty, 2) \cup (2, \infty) \) This graphical representation is vital for understanding restrictions on inputs that are critical for ensuring the function operates correctly.
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