Graph Transformation

Question

Sketch an accurate graph of the transformed function y = -1/2 * f(x – 1) + 2.

https://imgur.com/a/NNmrHIL

Write at least one sentence to explain how you developed the graph of the transformed function. Identify the point on the graph of the transformed function that corresponds to the original point (-2, 2).

Answer 1

y = -1/2 * f(x – 1) + 2

Transformations:

Start with the original function.

- : The negative means Flip over x-axis

1/2: The 1/2 means Shrink every point by cutting the heights in half (multiply by 1/2).

f(x-1): Shift entire graph Right 1 unit

+ 2: Shift entire graph Up 2 units

Point (-2, 2):

x = -2 >> Shift Right 1 to get x = -1

y = 2 >> Flip over x-axis to get -2, then Shrink by 1/2 to get -2*(1/2) = -1, then shift Up 2 to get -1 + 2 = 1

So, the new point is (-1, 1)

Answer 2

You can think about this in several steps.

if f(x) is your original function, then -1/2*f(x) is a stretch with scale factor -1/2 parallel to the y-axis. Hence all the y-values are multiplied by -1/2.

Then, -1/2*f(x-1) would translate the function one unit to the right. All x-values are increased by 1.

Finally, -1/2*f(x-1)+2 would translate the function two units upwards. All y-values are increased by 2.

Applying these transformations to the point (-2, 2) gives the following: After stretching becomes (-2, -1), after translating in the x-direction becomes (-1, -1), finally after translating in the y-direction becomes (-1, 1). So the point (-2, 2) is mapped to the point (-1, 1) under this transformation.

You can apply the same set of operations to some of the other points on the function to help you build a picture of the whole function transformed.