Function Transformations: Horizontal and Vertical Shifts

Identify the type of transformation: f(x) -> f(x) + 3

• Horizontal shift to the left

• Vertical shift downward

• Vertical shift upward

• Reflection over the x-axis

Tags

CCSS.HSF.BF.B.3

Apply a vertical translation of 5 units to the function f(x) = x^2

• f(x) = x^2 - 5

• f(x) = x^2 * 5

• f(x) = x^2 / 5

• f(x) = x^2 + 5

Graph the function g(x) = |x| and its transformation g(x) = |x| - 2

• Shift the graph of g(x) up by 2 units.

• Shift the graph of g(x) = |x| down by 2 units.

• Reflect the graph of g(x) over the x-axis.

• Stretch the graph of g(x) horizontally by 2 units.

Identify the type of transformation: f(x) -> f(x-4)

• Horizontal translation

• Vertical stretch

• Reflection over the x-axis

• Vertical translation

Apply a horizontal translation of 3 units RIGHT to the function f(x) = sqrt(x)

• f(x) = sqrt(x-3)

• f(x) = sqrt(x+3)

• f(x) = sqrt(x-1)

• f(x) = sqrt(x-5)

Tags

CCSS.HSF.BF.B.3

Graph the function h(x) = 2^x and its transformation h(x) = 2^(x+1)

• Stretch the graph of h(x) = 2^x vertically by a factor of 2

• Reflect the graph of h(x) = 2^x over the x-axis

• Shift the graph of h(x) = 2^x one unit to the right

• Shift the graph of h(x) = 2^x one unit to the left.