Transformations of functions

This course is a part of Algebra II, a 23-course Topic series from Khan Academy.

In Algebra 1, students reasoned about graphs of absolute value and quadratic functions by thinking of them as transformations of the parent functions |x| and x². In this unit, we extend this idea to include transformations of any function whatsoever. This fascinating concept allows us to graph many other types of functions, like square/cube root, exponential and logarithmic functions.

This course contains 8 segments:

Shifting functions

Learn how to transform functions so their graph is shifted horizontally or vertically. Learn how to find the equation of a function that is a shift of another function.

Reflecting functions

Symmetry of functions

You may already be familiar with types of symmetries of geometrical shapes. Learn how functions can be symmetrical too!

Scaling functions

Learn how to transform functions so their graph is stretched horizontally or vertically. Learn how to find the equation of a function that is a stretch of another function.

Putting it all together

Graphs of square and cube root functions

Learn how the graphs of radical functions look, and how we can reason about them using function transformations (i.e. shifts, stretches, etc.).

Graphs of exponential functions

Learn about the graphs of advanced exponential functions of the form y=a*b^(x+c)+d.

Graphs of logarithmic functions

Learn about the graphs of logarithmic functions, and how they relate to graphs of exponential functions.