Function Shifts

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

• f(x - 3)
• f(x + 3)
• f(x) + 3
• f(x) - 3

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

• f(x + 2)
• f(x) + 2
• f(x - 2)
• f(x) - 2

The original graph is f(x). The new graph has been reflected across the x axis. The equation for the new graph in f(x) notation is:

• -f(x)
• f(-x)

The original graph is f(x). The new graph is vertically stretched by a factor of 2. What is the equation for the new graph?

• 2f(x)
• f(2x)

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

• f(x + 3) - 4
• f(x - 4) + 3
• f(x + 4) + 3
• f(x + 3) + 4

The original graph is f(x). The new graph has been reflected across the y-axis and moved 6 to the right. Which of the following represents the new graph?

• f(x - 6)
• -f(x + 6)
• f(-x - 6)
• f(-x + 6)

The original graph is f(x). The new graph is up 5, left 3, and reflected across the x-axis.

• f(x + 3) + 5
• -f(x - 3) + 5
• -f(x + 3) + 5
• -f(x + 5) + 3

The original graph is f(x). The new graph has been vertically stretched by a factor of 4 and translated down 4.

• f(4x - 4)
• 4f(x -4)
• f(4x) - 4
• 4f(x) - 4

Name the parent function.

• Absolute Value
• Quadratic
• Square Root
• Linear

Name the parent function.

• Linear
• Quadratic
• Absolute Value
• Square Root