Find the domain of the following rational function. x+3 h(x) = x -9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain of h(x) is {x|x# ). (Type an integer or a fraction. Use a comma to separate answers as needed.) O B. There are no restrictions on the domain of h(x).
Quadratic Equation
When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.
Demand and Supply Function
The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.
![**Rational Functions: Determining the Domain**
When analyzing rational functions, it is important to determine the domain, which includes all possible input values (x-values) for which the function is defined. For the function given, certain values of \(x\) may cause the function to become undefined.
Given Rational Function:
\[ h(x) = \frac{x + 3}{x^2 - 9} \]
**Steps to Determine the Domain:**
1. **Identify the Denominator:**
The denominator of the function is \(x^2 - 9\).
2. **Set the Denominator to Zero:**
To find the values to exclude from the domain, set the denominator equal to zero and solve for \(x\).
\[
x^2 - 9 = 0
\]
\[
(x - 3)(x + 3) = 0
\]
\[
x = 3, \, -3
\]
3. **Exclude these Values from the Domain:**
The function becomes undefined when \(x = 3\) or \(x = -3\), so these values must be excluded from the domain.
**Choices:**
- **A.** The domain of \(h(x)\) is \(\{x | x \neq 3, -3\}\). (Type an integer or a fraction. Use a comma to separate answers as needed.)
- **B.** There are no restrictions on the domain of \(h(x)\).
For this function, the correct choice is **A** because the values \(x = 3\) and \(x = -3\) make the denominator zero, causing the function to be undefined.
**Conclusion:**
When determining the domain of a rational function, always solve for the values that make the denominator zero and exclude them from the domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1668cca6-eb9e-4ed5-b172-e483e25708ae%2Fae8bd9e0-53d3-4636-82fc-5654951cb185%2Fzw9pz3z_processed.jpeg&w=3840&q=75)
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