VCE Together Year 12 Mathematical Methods: Effect of Transformations

#### Mathematical Methods

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# Effect of Transformations

Effect of Transformations is part of the VCE Maths Methods course under the topic Functions and Graphs and sub-part Composite Functions, Transformations and Inverses. In this post, we will examine and apply transformations to sketch trigonometric functions of the form y=kf(a(x+b))+c , where a,b,c and k are constants, in a variety of contexts, where f(x) is one of \sin x, \cos x or \tan x , stating the domain and range when appropriate:

• Describe the effect of transformations on the graphs of a function or relation.
• Understand the relation between the graph of an original function and the graph of a corresponding transformed function.

### Transformations and graphs

In this video, we examine the relationship between our knowledge of transformations and the effect that these have on the function.

### Transformations of Trigonometric Functions

In this video, we will examine and apply transformations to functions, and see how the amplitude and period of a function can be affected and how a trigonometric function is vertically or phase-shifted.

### Sine and Cosine

Here, the graphing transformations are directly applied to the trigonometric functions of sine and cosine. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

### Tangent and Cotangent

Here, the graphing transformations are directly applied to the trigonometric functions of tangent and cotangent. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

### Secant and Cosecant

Here, the graphing transformations are directly applied to the trigonometric functions of secant and cosecant. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

Want to learn more? Check out more of our VCE Mathematics resources here!

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