Lesson Writing a function rule for a function based on its wording description
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<H2>Writing a function rule for a function based on its wording description</H2> <H3>Problem 1</H3>The functions f(x) and g(x) are sine functions, where f(0) = g(0) = 0. The amplitude of f(x) is twice the amplitude of g(x). The period of f(x) is one-half the period of g(x). If g(x) has a period of {{{2*pi}}} and {{{f(pi/4)}}} = 4, write the function rule for g(x). <B>Solution</B> <pre> According to the problem, functions g(x) is sinusoidal, has the value of 0 at x= 0 and has a period {{{2pi}}}. Hence, g(x) has the form g(x) = {{{b*sin(x)}}}, where real number "b" is the amplitude of g(x). Function f(x) is sinusoidal, has the value of 0 at x= 0 and has a period, which is one-half of that of g(x), i.e. {{{pi}}}. Hence, f(x) has the form f(x) = {{{a*sin(x/2)}}}, where real number "a" is the amplitude of f(x). Next, we are given {{{f(pi/4)}}} = 4. It means {{{a*sin(2*(pi/4))}}} = 4, or {{{a*sin(pi/2)}}} = 4. Since {{{sin(pi/2)}}} = 1, it gives us a = 4. It implies, due to the problem description, that the amplitude of g(x) is 2 : b = 2. Thus g(x) has the form g(x) = {{{2*sin(x)}}}. <U>ANSWER</U> </pre> My other lessons in this site on plotting and analyzing functions are - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Finding-x-intercepts-and-y-intercepts.lesson>Finding x-intercepts and y-intercepts</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Compressing-and-stretching-of-graphs.lesson>Compressing and stretching graphs</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/HOW-TO-PLOT-transformed-functions.lesson>HOW TO PLOT transformed functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/HOW-TO-write-functions-for-transformed-plots.lesson>HOW TO write functions for transformed plots</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/HOW-TO-PLOT-transformed-periodic-trigonometry-functions.lesson>HOW TO PLOT transformed periodic trigonometry functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Analyzing-periodic-trig-functions-for-amplitude-period-vert-and-hor-shifts.lesson>Analyzing periodic trigonometric functions for the amplitude, the period, vertical and horizontal shifts</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Do-not-fall-into-a-TRAP-when-analysing-problems-on-trigonometric-functions.lesson>Do not fall into a TRAP when analyzing problems on trigonometric functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/The-domain-and-the-range-of-transformed-functions.lesson>The domain and the range of transformed functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Write-a-function-that-has-given-transformations-from-the-parent-function.lesson>Write a function which is a result of given transformations of the parent function</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Describe-transformations-from-the-given-basic-function-to-final-function.lesson>Describe transformations from the given parent function to final function</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Constructing-a-function-based-on-its-given-properties.lesson>Constructing a function based on its given properties</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Finding-inverse-functions.lesson>Finding inverse functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Miscellaneous-problems-on-plots-of-functions.lesson>Miscellaneous problems on plots of functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Given-a-point-on-a-plot-of-a-function--find-the-corresponding-point-on-the-plot-of-transformed-function.lesson>Given a point on a plot of a function, find the corresponding point on the plot of transformed function</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Special-advanced-problems-on-finding-the-domain-of-functions.lesson>Special advanced problems on finding the domain of functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/Special-advanced-problems-on-finding-the-range-of-functions.lesson>Special advanced problems on finding the range of functions</A> - <A HREF=https://www.algebra.com/algebra/homework/Coordinate-system/OVERVIEW-of-lessons-on-plotting-and-analyzing-functions.lesson>OVERVIEW of lessons on plotting and analyzing functions</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-I. Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
