# VCE Mathematical Methods Units 3 and 4 – Functions and Graphs

1.1 Graphs

1.2 Exponential Graphs

1.3 Logarithmic Graphs

1.4 Trigonometric Graphs

1.5 Transformations

In this area of study students cover transformations of the plane and the behaviour of some elementary functions of a single real variable, including key features of their graphs such as axis intercepts, stationary points, points of inflection, domain (including maximal, implied or natural domain), co-domain and range, asymptotic behaviour and symmetry. The behaviour of these functions and their graphs is to be linked to applications in practical situations.

This area of study includes:

- graphs and identification of key features of graphs of the following functions:
- power functions, \( y = x^n , n ∈ Q \)
- exponential functions, \( y = a^x , a ∈ R^+\), in particular \( y = e^x \) , and logarithmic functions, \( y = \log_e (x) \) and \( y = \log_{10}(x) \)
- circular functions, \( y = \sin(x), y = \cos(x) \) and \( y = \tan(x) \)

- graphs of polynomial functions
- transformation from \( y = f(x) \) to \( y = Af(n(x + b)) + c\), where \(A, n, b \) and \( c ∈ R, A, n ≠ 0 \), and \( f \) is one of the functions specified above, and the inverse transformation the relation between the graph of an original function and the graph of a corresponding transformed function (including families of transformed functions for a single transformation parameter)
- graphs of sum, difference, product and composite functions where f and g are functions of the types specified above (not including composite functions that result in reciprocal or quotient functions), use of polynomial, power, circular, exponential and logarithmic functions, simple transformation and combinations of these functions, including simple piecewise (hybrid) functions, to model practical situations.

*source – VCE Mathematics Study Design*

VCE Mathematical Methods Units 3 and 4 Courses

VCE Mathematical Methods Units 3 and 4 Syllabus

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### Graphs

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Quartic Graphs
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Polynomial Graphs
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Exponential Graphs

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Logarithmic Graphs

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Trigonometric Graphs

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Transformations

Rotation of Curves
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Dilations
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