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If p assigns a quantity x to a second quantity, y, what is the range if p(x) = 3(x – 6)² + 11.2? (-00, 11.2]; y < 11.2 (-00, 6); y < 6 (-00, 00)

If p assigns a quantity x to a second quantity, y, what is the range if p(x) = 3(x – 6)² + 11.2? (-00, 11.2]; y < 11.2 (-00, 6); y < 6 (-00, 00)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** If \( p \) assigns a quantity \( x \) to a second quantity, \( y \), what is the range if \[ p(x) = 3(x - 6)^2 + 11.2? \] **Answer Choices:** - \((- \infty, 11.2]; \, y \leq 11.2\) - \((- \infty, 6]; \, y \leq 6\) - \((- \infty, \infty)\) - \([6, \infty); \, y \geq 6\) - \([11.2, \infty); \, y \geq 11.2\) *(correct choice indicated)* **Explanation:** The expression given is \( p(x) = 3(x - 6)^2 + 11.2 \). This represents a parabolic function that opens upwards because the coefficient of the squared term is positive. The vertex of the parabola is at the point \((6, 11.2)\), which means the minimum value of \( y \) is \( 11.2 \). Therefore, the range of the function is \([11.2, \infty)\).
Transcribed Image Text:**Problem Statement:** If \( p \) assigns a quantity \( x \) to a second quantity, \( y \), what is the range if \[ p(x) = 3(x - 6)^2 + 11.2? \] **Answer Choices:** - \((- \infty, 11.2]; \, y \leq 11.2\) - \((- \infty, 6]; \, y \leq 6\) - \((- \infty, \infty)\) - \([6, \infty); \, y \geq 6\) - \([11.2, \infty); \, y \geq 11.2\) *(correct choice indicated)* **Explanation:** The expression given is \( p(x) = 3(x - 6)^2 + 11.2 \). This represents a parabolic function that opens upwards because the coefficient of the squared term is positive. The vertex of the parabola is at the point \((6, 11.2)\), which means the minimum value of \( y \) is \( 11.2 \). Therefore, the range of the function is \([11.2, \infty)\).
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