Struggling to Graph with Respect to y? Tips and Tricks for TI-84 Users

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SUMMARY

This discussion addresses the challenges of graphing functions with respect to y using the TI-84 Plus Silver Edition (SE) calculator. The specific function in question is f(y) = y / √(16 - y²). Users are advised to graph the equivalent function y = f(x) = x / √(16 - x²) instead, as most graphing calculators only accept x as the independent variable. A practical tip shared is to physically rotate the calculator to visualize the graph correctly.

PREREQUISITES
  • Understanding of function notation and independent variables
  • Familiarity with the TI-84 Plus SE graphing calculator
  • Basic knowledge of square roots and their properties
  • Ability to manipulate equations to change the independent variable
NEXT STEPS
  • Learn how to graph parametric equations on the TI-84 Plus SE
  • Explore the use of online graphing tools like Desmos for visualizing complex functions
  • Study the properties of inverse functions and their graphical representations
  • Investigate the concept of implicit functions and how to graph them
USEFUL FOR

This discussion is beneficial for high school students, educators, and anyone using the TI-84 Plus SE who seeks to improve their graphing skills, particularly with respect to non-standard independent variables.

lLovePhysics
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Homework Statement


I'm having difficulty graphing with respect to y (unless I graph it point by point).

For example, I find it hard to graph: f(y)= \frac{y}{\sqrt{16-y^2}}


Does anyone know of an easy method to graph such a function or know how to do it on a Ti 84+ SE? Also, it would be great if someone could link me to a website that shows you a method. Thanks!
 
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Whenever you graph something, you need to first identify the independent and independent variables. In this case, y is the independent variable and f(y) is the independent variable so it is really no different than graphing an equation with x and f(x).

Most graphing calculators will only let you call the independent variable "x" and the independent variable "y" so this is a time when you just have to be smarter than the calculator.
 
Graph y= f(x)= \frac{x}{\sqrt{16-x^2}}
and then turn your calculator on its side!
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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