MTH1020 Study Guide - Final Guide: Unit Circle, Quintic Function, Moodle
6 Jun 2018
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Appendix: Background on functions
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Appendix: Background on functions
This appendix contains background material on functions which you are expected to know.
If you are not familiar with this material, please revise your notes from previous courses, or ask
through one of the many avenues for assistance available to you (moodle forum, Mathematics
Learning Centre, tutor, lecturer, etc).
Linear functions
A linear function is a function of the form , where are constants.
The linear function has gradient or slope given by
The graph of a linear function is a straight line; when increases by 1 unit,
increases by units.
The graph of the linear function has a single -intercept (unless
) and a single -intercept.
Polynomial functions
A polynomial function is a function of the form
where are constants.
The highest power of occurring in is called the degree of the polynomial.
Polynomials of degree 1, 2, 3, 4, 5 are called linear, quadratic, cubic, quartic, quintic
respectively.
The values of such that are called the roots of the polynomial .
The graph of a polynomial function of degree has at most -intercepts, occurring
at the roots of .
The graph of a polynomial function of degree has at most turning points.
Document Summary
This appendix contains background material on functions which you are expected to know. If you are not familiar with this material, please revise your notes from previous courses, or ask through one of the many avenues for assistance available to you (moodle forum, mathematics. Linear functions (cid:120) a linear function is a function of the form (cid:4666)(cid:4667)=+, where , are constants. (cid:120) the linear function (cid:4666)(cid:4667)=+ has gradient or slope given by. A rational function is a function of the form. For example, the following functions are rational functions: (cid:4666)(cid:4667)= (cid:4666)(cid:4667)(cid:4666)(cid:4667) where (cid:4666)(cid:4667) and (cid:4666)(cid:4667) are polynomials. This function is naturally defined at each such that (cid:4666)(cid:4667) (cid:882). (cid:2870)++(cid:885), (cid:883), (cid:2871)+(cid:883) (cid:884) (cid:883) You should be familiar with sin, cos and tan, including the following facts: Angle (cid:120) however, you should know these values of sin, cos and tan by drawing a picture, not by remembering the table!
