Transformations of Functions

Translations, reflections and stretches of y = f(x), combined as y = a·f(b(x − h)) + k, and inverses.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

The graph of y = f(x) is translated 3 units right and 2 units down. Which equation describes the new graph?
Which equation is the reflection of y = f(x) in the x-axis?
The point (8, 5) is on the graph of y = f(x). What is the x-coordinate of its image on the graph of y = f(4x)?
Compared with y = f(x), the graph of y = 3f(x) is:
The point P marked on the graph of y = f(x) is transformed by y = 2f(x − 1) + 3. What is the y-coordinate of the image of P?
Which list describes how y = −2f(3(x + 1)) − 4 is obtained from y = f(x)?
The point (−3, 6) is on the graph of y = f(x). What is the y-coordinate of its image on the graph of y = ½f(−x) + 1?
What is the inverse of f(x) = 2x − 6?
The graph of y = f(x) is shown. Which restriction on the domain of f keeps as much of the graph as possible and makes its inverse a function?
The function f(x) = (x − 2)² + 3, x ≥ 2, has an inverse. What is the value of f⁻¹(12)?