Transforming Functions SL

For the topic of transforming functions, we need to understand the effect of translating, reflecting and stretching has on functions. You may be asked to describe the transformations, sketch graphs or find the coordinates of points that have been transformed. Whilst technology can be a big help understanding these transformations, questions often require you to answer them without your graphical calculator.


Key Concepts

On this page, you should learn about

  • transformations of graphs
    • vertical translations: \(y=f(x)+b\) 
    • horizontal translations: \(y=f(x-a)\)
    • reflection in x axis: \(y=-f(x)\)
    • reflection in y axis: \(y=f(-x)\)
    • vertical stretch: \(y=af(x)\)
    • horizontal stretch: \(y=f(ax)\)
  • Compositions of any of the above transformations

Essentials

These graphs should help you understand the transformations of functions

Vertical Stretch y = af(x)

Drag the slider to see the effect

Horizontal Stretch y = f(ax)

Click on the image to open an applet and explore this transformation: 

Translations y = f(x - a) + b

Click on the image to open an applet and explore this transformation: 

Summary

Print from here

Test Yourself

Here is a quiz that practises the skills from this page


START QUIZ!

Exam-style Questions

Question 1

a) The following diagram shows the graph of a function f

On the same set of axes, sketch the graph of f(-x) + 2

You can print this graph from here

b)

The following diagram shows the function af(x+b)

Write down the values of a and b

Hint

Full Solution

Question 2

The graph of f(x) has a local maxima at \((1 - a , 2b)\) and a local minima at \((3a,b-3)\).

a) Find the coordinates of the local maxima of \(f(x+a)-2b\)

b) Find the coordinates of the local minima of \(2f(3x)\)

Hint

Full Solution

Question 3

Consider the function f(x) = x3 - 4x² - x + 6 , \(x \in \mathbb{R}\)

The graph of f is translated two units to the left and 3 units up to form the function g(x). Express g(x) in the form ax3 + bx² + cx + d where \(a,b,c,d \in \mathbb{Z}\)

Hint

Full Solution

Question 4

The graph of \(y=e^{2x-1}\) is obtained by performing two transformations to the function \(f(x)=e^x\)

- a stretch of scale factor a parallel to the x axis

- a stretch of scale factor b parallel to the y axis.

Find the values of a and b

Hint

Full Solution

MY PROGRESS

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