Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.) ex) = x² = 2x – 24 t(x) = X - 9 x-intercept (x, y) = (smaller x-value) x-intercept (x, y) = (larger x-value) y-intercept (x, y) =
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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.
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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.
![### Task 13: Finding x- and y-intercepts of a Rational Function
**Objective:**
Determine the x- and y-intercepts of the given rational function. If an answer does not exist, enter DNE (Does Not Exist).
**Given Function:**
\[ t(x) = \frac{x^2 - 2x - 24}{x - 9} \]
**Instructions:**
1. **x-intercepts:**
- Find the points where the function intersects the x-axis.
- These occur where \( t(x) = 0 \).
- Thus, solve the equation \( x^2 - 2x - 24 = 0 \).
2. **y-intercept:**
- Find the point where the function intersects the y-axis.
- This occurs where \( x = 0 \).
- Evaluate the function at \( x = 0 \) to find \( t(0) \).
**Input Fields:**
- **x-intercept (x, y) with smaller x-value:** \[ \boxed{\phantom{0}} \]
- **x-intercept (x, y) with larger x-value:** \[ \boxed{\phantom{0}} \]
- **y-intercept (x, y):** \[ \boxed{\phantom{0}} \]
**Options:**
- Optional submission of detailed work to support your answers. Use the "Show My Work (Optional)" section if necessary.
After completing your calculations, submit your answers through the "Submit Answer" button.
> Note: For this function, consider any possible factors or solutions that may not exist by entering DNE.
**Example Explanation:**
1. **Finding x-intercepts:**
- Factorize the numerator \( x^2 - 2x - 24 \).
- Solve for \( x \).
2. **Finding y-intercept:**
- Substitute \( x = 0 \) into the function.
- Simplify to find \[ t(0) \].
**Submit Answer:**
\[ \boxed{ \text{Submit Answer} } \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f4719ec-89c6-49f2-a8fd-c905fe776b01%2Fa5de0555-40b3-4a2a-b61e-e8490b8ce346%2Fbrcclt5_processed.jpeg&w=3840&q=75)
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