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The graph of a function in practice

Solving exercises about graphs of functions in the cartesian plane.

The following exercises are solved in this step.

We invite you to try to solve them before watching the video.

In any case, you will find below a PDF file with the solutions.

Exercise 1.

Prove that the functions [f:xmapsto x^3,quad g:xmapsto 2x^3,quad h:xmapsto frac 12 x^3,] are strictly increasing and odd, and the functions [f’:xmapsto -x^3,quad g’:xmapsto -2x^3,quad h’:xmapsto -frac 12 x^3] are strictly decreasing and odd.

Exercise 2. [Solved only in the PDF file]

Prove that the functions [f:xmapsto x^3+2,quad g:xmapsto x^3-2,quad h:xmapsto (x+2)^3,quad i:xmapsto (x-2)^3] are strictly increasing. Are they odd?

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Precalculus: the Mathematics of Numbers, Functions and Equations

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