Combining transformations of functions

All You Need in One Place

Everything you need for Year 6 maths and science through to Year 13 and beyond.

Learn with Confidence

We’ve mastered the national curriculum to help you secure merit and excellence marks.

Unlimited Help

The best tips, tricks, walkthroughs, and practice questions available.

0/5
?
Examples
Lessons
  1. Describe the Combination of Transformations
    Compared to y=f(x)y = f\left( x \right), describe every step of transformations applied to:
    y=2f[3(x+4)]+5y = - 2f\left[ {3\left( {x + 4} \right)} \right] + 5
    1. Write the Equation of a Transformed Function
      Transform the function f(x)=1xf\left( x \right) = \frac{1}{x} into the function g(x)g\left( x \right) by:
      1. stretching horizontally by a factor of 2 about the y-axis
      2. stretching vertically by a factor of 35\frac{3}{5} about the x-axis
      3. vertical translation of 7 units up
      4. reflection in the y-axis
      5. horizontal translation of 4 units to the left
      6. reflection in the x-axis

        Write the function for g(x)g(x).
    2. Use "Coordinate Mapping Formula" to Graph a Transformed Function
      Given the graph of y=f(x)y = f\left( x \right) as shown,
      1. describe every step of transformations applied to: y=14f(3x2)1y = \frac{1}{4}f\left( {3 - \frac{x}{2}} \right) - 1
      2. Graph the transformed function on the same set of coordinate axes.
      3. Shortcut: use "Coordinate Mapping Formula" to graph the transformed function.
        Combining transformations of functions