Graph Transformations

Flashcards about graph transformations based on lecture notes.

Vertical shift y = f(x) + c

Raise the graph of f(x) by c units

Vertical shift y = f(x) - c

Lower the graph of f(x) by c units

Horizontal shift y = f(x + c)

Shift the graph f(x) to the left c units

Horizontal shift y = f(x - c)

Shift the graph f(x) to the right c units

Reflection about the x-axis y = -f(x)

Reflect the graph of f(x) about the x-axis

Reflection about the y-axis y = f(-x)

Reflect the graph of f(x) about the y-axis

Vertical stretching and compression y = cf(x), c > 1

Vertically stretching the graph of f(x) (c > 1)

Vertical stretching and compression y = cf(x), 0 < c < 1

Vertically compressing the graph of f(x) (0 < c < 1)

Horizontal stretching and compression y = f(cx), c > 1

Horizontally compressing the graph of f(x) (c > 1)

Horizontal stretching and compression y = f(cx), 0 < c < 1

Horizontally stretching the graph of f(x) (0 < c < 1)

y = 1/f(x)

Take the reciprocal of each y coordinate of f(x)