Finding the Range of a Function Using Graphs

[mathdad]

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?

 

[skeeter]

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]

 

[mathdad]

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.

 

[skeeter]

if you can find the inverse ... sometimes easier said than done

 

[mathdad]

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.

 

[Greg]

Not all functions have an inverse. Calculus provides several tools for sketching the graph of a function.

 

[mathdad]

Thank you everyone for your help. You will see less questions from now on as I use the free youtube clips to review precalculus.