Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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third function h(x) is defined by the formula h(x) = x ^ 3 - 3 What is the value of g(h(2))? Show how you arrived at your answer .
The image appears to contain a set of mathematical problems related to functions and intervals. Below are the detailed transcriptions and explanations: **Questions:** (c) *Determine the intervals over which the function f(x) is increasing.* Options: 1. \(-7 < x < -3\) 2. \(3 < x < 5\) (circle around this option) 3. \(-5 < x < 5\) 4. \(-5 < x < 3\) (d) *State the coordinates of the relative maximum and the relative minimum of this function.* - Relative Maximum: ____________ - Relative Minimum: ____________ (f) *A second function \(g(x)\) is defined using the rule \(g(x) = 2f(x) + 5\). Evaluate \(g(0)\) using this rule. What does this correspond to on the graph of \(g\)?* (e) *Over which of the following intervals is \(f(x) < 0\)?* Options: 1. \(-7 < x < -3\) 2. \(2 \leq x \leq 7\) 3. \(-5 < x < 2\) 4. \(-5 \leq x \leq 2\) (g) *A third function \(h(x)\) is defined by the formula \(h(x) = -x^3 - 3\). What is the value of \(g(h(2))\)? Show how you arrived at your answer.* There are no graphs or diagrams included in the image. The tasks mainly involve analyzing function behavior, such as identifying intervals where a function is increasing or has certain sign properties, and applying transformations to functions.
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Transcribed Image Text:The image appears to contain a set of mathematical problems related to functions and intervals. Below are the detailed transcriptions and explanations: **Questions:** (c) *Determine the intervals over which the function f(x) is increasing.* Options: 1. \(-7 < x < -3\) 2. \(3 < x < 5\) (circle around this option) 3. \(-5 < x < 5\) 4. \(-5 < x < 3\) (d) *State the coordinates of the relative maximum and the relative minimum of this function.* - Relative Maximum: ____________ - Relative Minimum: ____________ (f) *A second function \(g(x)\) is defined using the rule \(g(x) = 2f(x) + 5\). Evaluate \(g(0)\) using this rule. What does this correspond to on the graph of \(g\)?* (e) *Over which of the following intervals is \(f(x) < 0\)?* Options: 1. \(-7 < x < -3\) 2. \(2 \leq x \leq 7\) 3. \(-5 < x < 2\) 4. \(-5 \leq x \leq 2\) (g) *A third function \(h(x)\) is defined by the formula \(h(x) = -x^3 - 3\). What is the value of \(g(h(2))\)? Show how you arrived at your answer.* There are no graphs or diagrams included in the image. The tasks mainly involve analyzing function behavior, such as identifying intervals where a function is increasing or has certain sign properties, and applying transformations to functions.
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