Exponential and Logarithmic Functions

Area of Study- Functions and Graphs (Unit 2)

In this area of study students cover graphical representation of functions of a single real variable and the key features of graphs of functions such as axis intercepts, domain (including maximal, natural or implied domain), co-domain and range, asymptotic behaviour, periodicity and symmetry.

Area of Study- Algebra (Unit 2)

This area of study supports students’ work in the ‘Functions and graphs’, ‘Calculus’ and ‘Probability and statistics' areas of study. In Unit 2 the focus is on the algebra of some simple transcendental functions and transformations of the plane. This area of study provides an opportunity for the revision, further development and application of content prescribed in Unit 1, as well as the study of additional algebra material introduced in the other areas of study in Unit 2.

Key skills and knowledge (as outlined in the 2016-2021 VCAA Mathematics Study Design Outcome 1)

• the effect of transformations of the plane on the graphs of sine, cosine, tangent and exponential functions
• characteristics of data which suggest the use of sine, cosine, exponential or logarithmic functions as an appropriate type of model for a given context
• the key features of the exponential and logarithmic functions and their graphs
• the relationship between an exponential function to a given base and the logarithmic function to the same base as inverse functions
• sketch by hand graphs of the sine, cosine and exponential functions, and simple transformations of these to the form Af (bx) + c, and sketch by hand graphs of log_a(x) and the tangent function
• draw graphs of circular, exponential and simple logarithmic functions over a given domain and identify and discuss key features and properties of these graphs
• describe the effect of transformations of the plane on the graphs of the sine, cosine, tangent and exponential functions, and apply matrices to transformations, by hand in simple cases
• solve simple equations over a specified interval related to circular, exponential and simple logarithmic functions using graphical, numerical and analytical approaches

Assessment Overview

Topic tests will assess:

• key knowledge and skills,
• ability to problem-solve and use the mathematics in context,
• use of the CAS, to assist problem-solving