Lesson Miscellaneous problems on plots of functions
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<H2>Miscellaneous problems on plots of functions</H2> <H3>Problem 1</H3>Let f(x)= {{{sqrt(x)}}}. Find g(x), the function that has the plot reflected over the x-axis and stretched horizontally by a factor of 6. <B>Solution</B> Stretching is the action opposite to compressing. <pre> To reflect the plot f(x) = {{{sqrt(x)}}} over the x-axis means to change the sign of the function. So {{{sqrt(x)}}}, reflected over x-axis is {{{-sqrt(x)}}}. Next, the function {{{-sqrt(x)}}}, stretched horizontally by a factor of 6 is {{{-sqrt(x/6)}}}. So, the function g(x) = {{{-sqrt(x/6)}}} is your <U>ANSWER</U>. </pre> <H3>Problem 2</H3>Suppose (5,−5) is a point on the graph of y = f(x). What is a point that will be on the graph of y = −6f(x)+6? <B>Solution</B> <pre> The plot of y = -6f(x) + 6 is obtained from the parent plot y = f(x) by stretching y-axis 6 times, then reflecting about x-axis and then shifting 6 units up. THEREFORE, since the point (5,-5) was originally on the parent plot y = f(x), we FIRST move this point to the new position (5,-30), THEN reflect this point (5,-30) about x-axis, getting the point (5,30), and AFTER THAT we move this point (5,30) six units up, getting finally the point (5,36). This procedure does not depend on what the function f(x) is concretely: it works for ANY function f(x). </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/Writing-a-function-rule-for-a-function-based-on-its-wording-description.lesson>Writing a function rule for a function based on its wording description</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/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.
