Transformation of Graphs - for GCSE, IB and A Level

 Transformation of Graphs - GCSE, IGCSE, GCE-OL, GCE-AL, A Level & IB

Functions - f(x)

f(x) = 2x - 3 is called a function of x. Whatever you put inside the parentheses on the left, must replace the variable, x in this case, on the right.

E.g.

f(2) = 2(2) - 3 = 1

f(0) = 2(0) - 3 = -3

f(-2) = 2(-2) - 3 = -7

f(x+1) = 2(x+1) - 3 = 2x - 1

f(x²) = 2(x²) - 3 = 2x² - 3

f(x/2) = 2(x/2) - 3 = x - 3

f(-x) = 2(-x) - 3 = -2x - 3

-f(x) = -(2x - 3) = -2x + 3

Transformation of Graphs 

There are three transformations. They are:

1. Translation
2. Reflection
3. Stretching

With this Chrome browser extension, you can transform the following graphs:

1. Linear graphs - e.g. f(x) = 2x - 3
2. Quadratic graphs - e.g. f(x) = x² - 2x
3. Cubic graphs - e.g. f(x) = x^3
4. Reciprocal graphs - e.g. f(x) = 1/x
5. Exponential graphs - e.g. f(x) = 2^x
6. Trigonometric graphs - e.g. f(x) = sin(x)

Translation

Translation in the x-axis: f(x) → f(x ± a)

Translation in the x-axis

Translation in the y-axis: f(x) → f(x) ± a

Translation in the y-axis

Reflection

• Reflection in the x-axis: f(x) → -f(x)
• Reflection in the y-axis: f(x) → f(-x)

Reflection in the x-axis and y-axis

Stretching 

Stretching parallel to x-axis: f(x) → f(ax)

Stretching parallel to y-axis: f(x) → af(x)

Stretching parallel to x-axis and y-axis

This is the Chrome browser extension at play:

Chrome browser extension for transformation of graphs