Question

. Describe the transformation of the function, y = x + 4, from y = x.

Answer 1

There are two interpretations we could go for:

1. Adding 4 to the end means we add 4 to each y coordinate (since y = x). This shifts the entire line 4 units up
2. Replacing x with x+4 means the xy axis is shifted 4 units to the right. If the line y = x is held completely still while the axis moves, then it gives the illusion the line is moving 4 units to the left

Check out the diagram below.

Point A on the red line y = x has two locations it could end up. If we follow method 1, then point A shifts upward to point B. Do this to every point on the red line and the entire red line shifts up 4 units.

Or if you decide to shift 4 units to the left (method 2), then point A moves to point C's location. Doing this to every point on the red line shifts the entire line 4 units to the left.