Transforming graphs GCSE lesson: translations and reflections of y = f(x)

Transforming graphs: practice

Show your working: for each move, say whether x or y changes. The stretch is optional.

Diagnostic question: choose and explain

1. y = x² is moved to y = (x − 4)². How did it move?
   1. 4 to the right
   2. 4 to the left
   3. 4 up
   4. 4 down

Practice questions

1. y = f(x) + 5 is y = f(x) moved…
   1. 5 up
   2. 5 to the right
   3. 5 to the left
2. (3, 2) is on y = f(x). On y = f(x) − 4 it goes to (3, ___)
3. (3, 2) is on y = f(x). On y = f(x + 1) it goes to (___, 2)
4. y = x² moved 3 to the left is y = (x + ___)²
5. y = x² is reflected in the y-axis, giving y = (−x)². What happens to the curve?
   1. Nothing: it is the same curve
   2. It turns upside down
   3. It moves to the left
6. y = −f(x) is y = f(x) reflected in which axis?
   1. The x-axis
   2. The y-axis
7. x² − 6x + 11 = (x − 3)² + 2, so y = x² − 6x + 11 is y = x² moved by the vector (___, ___)
8. Stretch: y = f(x) has its lowest point at (1, −3). The lowest point of y = f(x − 2) + 5 is (___, ___)

Support: For question 3: f(x + 1) is inside the bracket, so only x changes, the opposite way to the sign. Which way, and how far?

Transforming graphs: exit

A vector and one sentence are enough.

1. y = x² is moved to y = (x + 2)² − 1. Describe the move as a vector, and say where the lowest point goes, and why.

Exit check

One description and one point show who reads inside and outside correctly.

y = x² is moved to y = (x + 2)² − 1. Describe the move as a vector.

Transforming graphs: moves and points

For each move, say whether x or y changes, and which way. Give translations as vectors.