MathTrackX: Special Functions

Overview

This course is part two of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.

Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will continue the study of functions initiated in the course Polynomials, Functions and Graphs by moving into trigonometric functions, exponential functions, and logarithmic functions.

Trigonometric functions are extremely important in applications of mathematics to study situations involving periodic phenomena such as tidal flow. Exponential and logarithmic functions have many uses in applications of mathematics to biology, business and economics, physics and other areas.

Join us as we provide opportunities to develop your skills and confidence in applying mathematical functions.

Syllabus

Section 1: Exponential functions

» Establish and use the algebraic properties of exponential functions

» Recognise the qualitative features of the graph of exponentials including asymptotes

» Identify contexts suitable for modelling with exponential functions and use them to solve practical problems.

Section 2: Logarithmic functions

» Recognise and use the inverse relationship between logarithms and exponentials

» Establish and use algebraic properties of logarithms

» Interpret and use logarithmic scales

» Recognise qualitative features of the graph of y=a(x) (with a>1) including asymptotes, and more generally y=a(x+c)+b.

» Identify contexts suitable for modelling with logarithmic functions and use them to solve practical problems (algebraically, graphically, and with technology).

Section 3: Trigonometric functions

» Understand the unit circle definition of sin, cos and tan using radians and recognise the exact values at integer multiples of pi/6 and pi/4

» Recognise the graphs of y=cos(x), y=sin(x), y=tan(x) and identify key elements of their graphs

» Describe amplitude, period and phase changes of sin, cos and tan, and graphs of y=asin(bx+c)+d, y=acos(bx+c)+d, y=a tan(bx+c)+d

» Prove and apply common trigonometric identities including angle sum and angle difference identities

» Identify contexts suitable for modelling with trigonometric functions and use them to solve practical problems.

Section 4: Reciprocal and absolute value functions

» Recognise the shape of the graph of a reciprocal function

» Recognise the shape of the graph of an absolute value function

» Apply the properties of absolute values, and use them to solve equations.

» Describe the effect of performing the absolute value on an existing function

Section 5: Assessment