Function Transformations

"Not a lot of people know this, but I'm very good at mathematics. When I was an angry teenager, I used to sit in my room and do quadratic equations to calm myself down "

Samantha Bond

Translations

What you have to know:

Understand basic functions such as \(y=x^2\), \(y=x^3\), \(y=\sqrt{x}\), \(y=|x|\), and \(y=\frac1x\).
Be able to plot simple functions using a GDC.

Key Points

1. Watch the video:

A translation moves a graph without changing its shape.

Reflections

What you have to know:

Recognise the effect of negative signs inside and outside a function.

Key Points

1. Watch the video:

Stretches and Compressions

What you have to know:

Understand the difference between horizontal and vertical transformations.

Key Points

1. Watch the video:

Combined Transformations

What you have to know:

Be confident with individual transformations before combining them.

Key Points

1. Watch the video:

Extra

Material and references:

Hodder Mathematics AA SL:
Functions and Transformations Chapter

Key Points

1. A translation by \(a\) units horizontally and \(b\) units vertically:
\[ y=f(x-a)+b \]
2. Reflection in the \(x\)-axis:
\[ y=-f(x) \]
3. Reflection in the \(y\)-axis:
\[ y=f(-x) \]
4. Vertical stretch by factor \(k\):
\[ y=kf(x) \]
5. Horizontal stretch by factor \(k\):
\[ y=f\left(\frac{x}{k}\right) \]
6. Remember: transformations inside the bracket affect the graph horizontally, while transformations outside the bracket affect the graph vertically.
7. The order of transformations matters when several transformations are combined.

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