Changes outside the function move the graph up or down or stretch it vertically. y = f(x) + 3 moves every point up 3. y = −f(x) reflects the graph in the x-axis. y = 2f(x) doubles every y-coordinate.
Changes inside the function act on x, and they work the opposite way. y = f(x + 3) moves the graph 3 to the left. y = f(−x) reflects it in the y-axis. So the point (3, 3) on y = f(x) moves to (0, 3) on y = f(x + 3).
Worked example
(1, −5) lies on y = f(x). Where does it move on y = f(x) − 4?
- Outside change: affects y only.
- −5 − 4 = −9.
Answer:(1, −9)
Key words
- translation
- a slide
- reflection
- a flip in an axis
- stretch
- a change of scale in one direction
Practise this
New questions every time.
Common Core-referenced: HSF-BF.B.3