Find a power function, f(x), satisfying the following. a) The points (2, 2) and lie on the graph of fx) = b) x 2 3 5 f(x) 128 972 12500 f(x) = %3D
Find a power function, f(x), satisfying the following. a) The points (2, 2) and lie on the graph of fx) = b) x 2 3 5 f(x) 128 972 12500 f(x) = %3D
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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,...
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![**Power Function Exploration**
**Task:** Find a power function, \( f(x) \), satisfying the given conditions.
**a) Conditions:**
The points \( (2, 2) \) and \( \left( \frac{1}{3}, \frac{1}{18} \right) \) lie on the graph of \( f(x) \).
\( f(x) = \) [________ ]
**b) Data Points Table:**
| \( x \) | \( 2 \) | \( 3 \) | \( 5 \) |
|---------|---------|---------|---------|
| \( f(x) \) | \( 128 \) | \( 972 \) | \( 12500 \) |
\( f(x) = \) [________ ]
**Instructions:**
- For part (a), find a function \( f(x) \) that passes through the given points. Use the provided information to determine the parameters of the power function.
- For part (b), use the table to deduce the power function that fits the given data points. Analyze the relationship between \( x \) and \( f(x) \) to identify the correct mathematical form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70d544f3-af03-440f-8854-80f7a0fb58cd%2F2243e348-d395-49bd-b58f-38afa73fa684%2F2v4ftqo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Power Function Exploration**
**Task:** Find a power function, \( f(x) \), satisfying the given conditions.
**a) Conditions:**
The points \( (2, 2) \) and \( \left( \frac{1}{3}, \frac{1}{18} \right) \) lie on the graph of \( f(x) \).
\( f(x) = \) [________ ]
**b) Data Points Table:**
| \( x \) | \( 2 \) | \( 3 \) | \( 5 \) |
|---------|---------|---------|---------|
| \( f(x) \) | \( 128 \) | \( 972 \) | \( 12500 \) |
\( f(x) = \) [________ ]
**Instructions:**
- For part (a), find a function \( f(x) \) that passes through the given points. Use the provided information to determine the parameters of the power function.
- For part (b), use the table to deduce the power function that fits the given data points. Analyze the relationship between \( x \) and \( f(x) \) to identify the correct mathematical form.
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