Graph translation

Question 1

describe the transformation of
y = f(x) + a

Answer 1

a vertical translation up a units
(x, y) → (x, y + a)

Question 2

describe the transformation of
y = f(x) - a

Answer 2

a vertical translation down a units
(x, y) → (x, y - a)

Question 3

describe the transformation of
y = f(x + a)

Answer 3

a horizontal translation left a units
(x, y) → (x - a, y)

Question 4

describe the transformation of
y = f(x - a)

Answer 4

a horizontal translation right a units
(x, y) → (x + a, y)

Question 5

describe the transformation of
y = - f(x)

Answer 5

reflection over the x-axis
(x, y) → (x, - y)

Question 6

describe the transformation of
y = f(- x)

Answer 6

reflection over the y-axis
(x, y) → (- x, y)

Question 7

describe the transformation of
y = af(x)

Answer 7

a vertical stretch by factor a
(x, y) → (x, ay)

Question 8

describe the transformation of
y = f(ax)

Answer 8

a horizontal compression by factor 1/a
(x, y) → (x / a, y)