Math Problem Statement
The function g is related to a parent function f(x) = sin(x). g(x) = sin(2x β π) (a) Describe the sequence of transformations from f to g. The function g(x) is obtained by a ---Select--- of 2 and a ---Select--- of π 2 to the right. (b) Sketch the graph of g.
The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 4π. One cycle starts on the x-axis at x = 0, goes down and right becoming less steep, changes direction at the point (π, β1), goes up and right becoming more steep, crosses the x-axis at x = 2π, goes up and right becoming less steep, changes direction at the point (3π, 1), goes down and right becoming more steep, and stops on the x-axis at x = 4π. The next cycle starts at x = 4π.
The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every 4π. One cycle starts on the x-axis at x = 0, goes down and right becoming less steep, changes direction at the point (π, β2), goes up and right becoming more steep, crosses the x-axis at x = 2π, goes up and right becoming less steep, changes direction at the point (3π, 2), goes down and right becoming more steep, and stops on the x-axis at x = 4π. The next cycle starts at x = 4π.
The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every π. One cycle starts on the x-axis at x = 0, goes down and right becoming less steep, changes direction at the point (πβ4, β1), goes up and right becoming more steep, crosses the x-axis at x = πβ2, goes up and right becoming less steep, changes direction at the point (3πβ4, 1), goes down and right becoming more steep, and stops on the x-axis at x = π. The next cycle starts at x = π.
The x y-coordinate plane is given. A curve has a cycle that repeats horizontally every π. One cycle starts on the x-axis at x = 0, goes down and right becoming less steep, changes direction at the point (πβ4, β2), goes up and right becoming more steep, crosses the x-axis at x = πβ2, goes up and right becoming less steep, changes direction at the point (3πβ4, 2), goes down and right becoming more steep, and stops on the x-axis at x = π. The next cycle starts at x = π.
(c) Use function notation to write g in terms of f. g(x) = fβ
Solution
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Transformations of functions
Formulas
g(x) = sin(2x - Ο)
f(x) = sin(x)
g(x) = f(2x - Ο)
Theorems
Trigonometric transformations
Sine function period and phase shift
Suitable Grade Level
Grades 10-12
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