Function Transformations
Shifts, stretches and reflections of graphs.
Key idea
Shifts, stretches and reflections of graphs.
In depth
f(x) + k shifts up, f(x − h) shifts right, −f(x) reflects over the x-axis, a·f(x) stretches vertically. Changes inside the function act on x and often behave the opposite of what you expect.
Worked example
y = (x + 2)² − 3 is y = x² shifted 2 left and 3 down.
Formula
Real-world uses
- Shifting and stretching graphs in computer graphics, sound equalisers and data visualisation
Common mistake
Moving the graph the wrong way for horizontal shifts.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Function Transformations?
Shifts, stretches and reflections of graphs. It is a topic at the advanced level in Algebra.
What is the formula for Function Transformations?
The key formula is y = a·f(x−h)+k.
Where is Function Transformations used in real life?
Real-world examples: Shifting and stretching graphs in computer graphics, sound equalisers and data visualisation.
What should I learn before Function Transformations?
Make sure you are comfortable with Absolute Value Functions, the previous topic in Algebra.
What is a common mistake with Function Transformations?
Moving the graph the wrong way for horizontal shifts.
How can I practise Function Transformations?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Function Transformations?
Move on to Function Composition next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.