Find the domain of the following function. Do not use a graphing calculator f(x) = 1 x2 - 5x - 6 The domain is (Type your answer in interval notation.) ***

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Finding the Domain of a Rational Function**

**Problem Statement**
Find the domain of the following function. Do not use a graphing calculator.

**Function**
\[ f(x) = \frac{1}{x^2 - 5x - 6} \]

**Instructions**
Determine the domain of the function by identifying the values of \( x \) for which the denominator is not equal to zero. Provide your answer in interval notation.

**Domain Answer Box**
\[ \text{The domain is } \_\_\_\_\_ \]
*(Type your answer in interval notation.)*

**Tools and Resources**
- View an example
- Get more help

**User Interface Elements**
- "Clear all" button
- "Skill builder" button

Explore the steps to find the domain:
1. Set the denominator equal to zero: \( x^2 - 5x - 6 = 0 \).
2. Solve for \( x \) where the function is undefined.
3. Exclude these \( x \)-values from the real number set to determine the domain.
4. Express the domain using interval notation.

**Solution Outline**
1. Factor the quadratic equation \( x^2 - 5x - 6 = 0 \) to find the critical points where the function is undefined.
2. Identify the intervals where the function is defined.
3. Write these intervals in interval notation as the domain.
Transcribed Image Text:**Finding the Domain of a Rational Function** **Problem Statement** Find the domain of the following function. Do not use a graphing calculator. **Function** \[ f(x) = \frac{1}{x^2 - 5x - 6} \] **Instructions** Determine the domain of the function by identifying the values of \( x \) for which the denominator is not equal to zero. Provide your answer in interval notation. **Domain Answer Box** \[ \text{The domain is } \_\_\_\_\_ \] *(Type your answer in interval notation.)* **Tools and Resources** - View an example - Get more help **User Interface Elements** - "Clear all" button - "Skill builder" button Explore the steps to find the domain: 1. Set the denominator equal to zero: \( x^2 - 5x - 6 = 0 \). 2. Solve for \( x \) where the function is undefined. 3. Exclude these \( x \)-values from the real number set to determine the domain. 4. Express the domain using interval notation. **Solution Outline** 1. Factor the quadratic equation \( x^2 - 5x - 6 = 0 \) to find the critical points where the function is undefined. 2. Identify the intervals where the function is defined. 3. Write these intervals in interval notation as the domain.
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