Exercises for Question Type 4: Creating a description explaining function transformations

Question 1

For the function y = 5 sin (2 x - 6), determine the x -coordinate of the first local minimum after x = 3 .

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Question 2

Find the derivative \frac{d y}{d x} of y = 5 sin (2 x - 6) and determine the x -values where this derivative is zero for 3 \leq x \leq 3 + π .

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Question 3

What is the equation of the midline of the function y = 5 sin (2 x - 6)?

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Question 4

This question requires solving a trigonometric equation over a given interval, involving a horizontal shift and a change in period. Students must find all solutions within the domain [0, 2 π] .

Solve the equation 5 sin (2 x - 6) = 3 for 0 \leq x \leq 2 π .

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Question 5

Find the range of the function y = 5 sin (2 x - 6) .

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Question 6

Express the function y = 5 sin (2 x - 6) in the form y = A sin (B (x - C)) + D by identifying A, B, C, and D .

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Question 7

Find the x -intercepts of y = 5 sin (2 x - 6) within the interval [0, 2 π] .

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Question 8

Transformations of trigonometric functions.

Describe in words how the graph of y = sin (x) changes when it is transformed into y = 5 sin (2 x - 6) .

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Question 9

Starting from y = sin (x), write the equation of the function after applying a horizontal compression by a factor of \frac{1}{2}, a horizontal shift right by 3 units, and a vertical stretch by a factor of 5.

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Question 10

Find the equation of the function obtained by transforming the graph of y = sin (x) such that it has an amplitude of 5, a period of π, a phase shift of 3 units to the right, and no vertical shift.

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Question 11

Determine the smallest positive period of y = 5 sin (2 x - 6) .

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Question 12

A point moves according to the law y = 5 sin (2 x - 6) . Find the smallest positive x such that y = - 5 .

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Question 13

Sketch one period of y = 5 sin (2 x - 6) and label all maximum, minimum, and x -intercept points.

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Question 14

Functions: Transformations of graphs

Describe the sequence of transformations that maps the graph of y = sin (x) to the graph of y = 5 sin (2 x - 6) .

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Question 15

Determine all x -values (general form) for which y = 5 sin (2 x - 6) attains its maximum value.

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Question 16

State the amplitude, period, phase shift, and vertical shift of the function y = 5 sin (2 x - 6) .

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IB Mathematics Applications & Interpretation Question Type 4: Creating a Description Explaining Function Transformations Exercises