Still Confused?

Try reviewing these fundamentals first

- Home
- Sixth Year Maths
- Transformations of Functions

Still Confused?

Try reviewing these fundamentals first

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started NowStart now and get better maths marks!

Get Started Now- Lesson: 144:31
- Lesson: 212:09

Horizontal translations refer to movements of a graph of a function horizontally along the x-axis by changing the x values. So, if y = f(x), then y = (x –h) results in a horizontal shift. If h > 0, then the graph shifts h units to the right; while If h < 0, then the graph shifts h units to the left.

Basic Concepts: Completing the square, Converting from general to vertex form by completing the square, Shortcut: Vertex formula

Related Concepts: Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs

Compared to $y=f(x)$:

$y=f(x-8)$: shift 8 units to the right

$y=f(x+3)$: shift 3 units to the left

$y=f(x-8)$: shift 8 units to the right

$y=f(x+3)$: shift 3 units to the left

- 1.a)Sketch the following functions on the same set of coordinate axes:

$y = {\left( x \right)^2}$ VS. $y = {\left( {x - 6} \right)^2}$ VS. $y = {\left( {x + 5} \right)^2}$b)Compared to the graph of $y = {x^2}$:

• the graph of $y = {\left( {x - 6} \right)^2}$ is translated "horizontally" ________ units to the ______________.

• the graph of $y = {\left( {x + 5} \right)^2}$ is translated "horizontally" ________ units to the ______________. - 2.
**Horizontal Translations**

Given the graph of $y = f\left( x \right)$ as shown, sketch:a)$y = f\left( {x-8} \right)$b)$y = f\left( {x+3} \right)$c)In conclusion:

• $\left( x \right) \to \left( {x-8} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________

• $\left( x \right) \to \left( {x+3} \right)$: shift __________ to the __________. All x coordinates $\Rightarrow$ ____________________

2.

Transformations of Functions

2.1

Transformations of functions: Horizontal translations

2.2

Transformations of functions: Vertical translations

2.3

Reflection across the y-axis: $y = f(-x)$

2.4

Reflection across the x-axis: $y = -f(x)$

2.5

Transformations of functions: Horizontal stretches

2.6

Transformations of functions: Vertical stretches

2.7

Combining transformations of functions

2.8

Even and odd functions

We have over 860 practice questions in Sixth Year Maths for you to master.

Get Started Now