Translations, Rotations, Shrinks And Stretches

Translations, Rotations, Stretches and Shrinks

horizontal: Let's use the basic functions y = x2 y = (x + 3)2

y = (x - 3)2

y = (2(x + 3))2

Title: Jul 23­7:29 AM (1 of 5)

y = (-x + 3)2

y = (2x + 3)2

y = (-(x + 3))2

vertical: Again, let's use the basic functions y = x2 y = (x)2 + 3

y = 2(x)2 + 3

Title: Jul 23­7:33 AM (2 of 5)

y = (x)2 - 3

y = -(x)2 + 3

y = -[(x)2 + 3]

y = -2(x)2 + 3

y = 2[(x)2 + 3]

y = -2[(x)2 + 3]

f(x) = -2(3(x - 1))2 + 2

Title: Jul 23­7:37 AM (3 of 5)

f(x) = -4[(2x - 1)2 + 2]

f(x) = 2(3x + 4)2 - 4

Title: Jul 23­7:37 AM (4 of 5)

f(x) = -(2(x + 2))2 - 1

The graph of y = x3 undergoes the following transformations, in order. Find the equation of the graph that results. a. a horizontal shrink by a factor of 1/3. b. a horizontal shift 2 units to the left.

The graph of y = sin x undergoes the following transformations, in order. Find the equation of the graph that results. a. a vertical shrink by a factor of 1/4. b. a vertical shift 2 units down c. a reflection over the x-axis d. a horizontal stretch by a factor of 3 e. a horizontal shift 2 units to the right

Title: Jul 23­7:46 AM (5 of 5)