Lesson Do not fall into a TRAP when analyzing problems on trigonometric functions

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Do not fall into a TRAP when analyzing problems on trigonometric functions

Problem 1

Describe what the graph of f(x) = -sin%283x-pi%29-2

would look like?
Address all numerical elements and their effects on the parent function.

Solution

Given function  f(x) =   is IDENTICAL to / (is the same as)

                f(x) = .


The parent function is  a(x) = sin(x).


Amplitude of f(x) is 1.


Period of f(x) is .


Phase shift of f(x) is  0  (zero).


Vertical shift is  -2  (2 units down).

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This problem is a TRAP : it has a huge underwater stone for unexperienced reader.

The sign "-" (minus) before sine and the shift by

in the argument
mutually annihilate each other, so the final function, actually, has no shift (!)

The meaning of the problem is to teach a reader recognizing
such traps to avoid falling into them in the future.

My other lessons in this site on plotting and analyzing functions are
    - Finding x-intercepts and y-intercepts
    - Compressing and stretching graphs
    - HOW TO PLOT transformed functions
    - HOW TO write functions for transformed plots
    - HOW TO PLOT transformed periodic trigonometry functions
    - Analyzing periodic trigonometric functions for the amplitude, the period, vertical and horizontal shifts
    - The domain and the range of transformed functions
    - Write a function which is a result of given transformations of the parent function
    - Describe transformations from the given parent function to final function
    - Writing a function rule for a function based on its wording description
    - Constructing a function based on its given properties
    - Finding inverse functions
    - Miscellaneous problems on plots of functions
    - Given a point on a plot of a function, find the corresponding point on the plot of transformed function
    - Special advanced problems on finding the domain of functions
    - Special advanced problems on finding the range of functions
    - OVERVIEW of lessons on plotting and analyzing functions

Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.

Use this file/link ALGEBRA-II - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-II.

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