Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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.
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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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