Skip main navigation

Hurry, only 2 days left to get one year of Unlimited learning for £249.99 £174.99. New subscribers only. T&Cs apply

Find out more

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?

This article is from the free online

Precalculus: the Mathematics of Numbers, Functions and Equations

Created by
FutureLearn - Learning For Life

Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now