Finding the Range of a Function Using Graphs

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SUMMARY

The discussion focuses on finding the range of the function y = 125 - 12x^3 using its graph. Participants confirm that the range is all real numbers, y ∈ (-∞, ∞), due to the nature of the cubic function. The conversation also highlights the challenges of finding inverses for more complex functions, with the suggestion to use Wolfram Alpha for assistance. Additionally, it emphasizes the importance of calculus tools for graphing functions effectively.

PREREQUISITES
  • Understanding of cubic functions and their graphs
  • Familiarity with the concept of function inverses
  • Basic knowledge of calculus for graph sketching
  • Experience with Wolfram Alpha for mathematical computations
NEXT STEPS
  • Learn how to graph cubic functions effectively
  • Study the properties of function inverses and their domains
  • Explore calculus techniques for sketching complex functions
  • Utilize Wolfram Alpha to find inverses of various functions
USEFUL FOR

Students and educators in precalculus, mathematicians dealing with function analysis, and anyone interested in mastering graphing techniques and function inverses.

mathdad
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Set 3.1
Question 16.

Find the range using the graph of y.

y = 125 - 12x^3

Obviously, I must graph the function as step one. How is the graph used to find the range?
 
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you look at the values of $y$ ... $y \in (-\infty,\infty)$

[DESMOS=-6.723253753255145,6.375413083862618,-819.3444017457867,753.6024560560803]y=125-12x^3;[/DESMOS]
 
From the graph, I can see that it is ok for y to be ALL REAL NUMBERS. Of course, this is an easy function. What about for complicated functions? Can I apply the method of taking the inverse? The domain of the inverse function is the range of the original.
 
if you can find the inverse ... sometimes easier said than done
 
You have made it clear that finding the inverse can sometimes be overwhelmingly difficult. In terms of complicated functions, I use wolfram to find the inverse.
 
Not all functions have an inverse. Calculus provides several tools for sketching the graph of a function.
 
Thank you everyone for your help. You will see less questions from now on as I use the free youtube clips to review precalculus.
 

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