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.