MHB Finding the Range of a Function Using Graphs

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To find the range of the function y = 125 - 12x^3, the graph is essential as it visually represents the values of y. The discussion confirms that for this specific function, the range is all real numbers, y ∈ (-∞, ∞). For more complex functions, finding the inverse can help determine the range, but it may be challenging. Tools like Wolfram Alpha can assist in finding inverses, though not all functions possess them. The use of calculus and online resources is encouraged for better understanding and graphing of functions.
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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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