Pre Calculus Transformations Lesson

Describe the Transformations of f(x):

y=2f(x - 3) - 4

• Vertical Stretch of 2, Left 3 units, Up 4 units

• Vertical Stretch of 1/2 , Right 3 units, Down 4 units

• Vertical Stretch of 2, Right 4 units, Down 3 units

• Vertical Stretch of 2, Right 3 units, Down 4 units

What transformations of y = x² would create the graph of

y = (x - 7)² + 9?

• translation down 7 and up 9

• translation left 7 and up 9

• translation right 7 and up 9

• translation right 7 and down 9

Which function would show a reflection across the x-axis, a vertical stretch of 4 and a horizontal translation left 6?

• f(-4x) + 6

• -4f(x + 6)

• -f(1/4 x - 6)

• f(-4x - 6)

What transformations change y = x² into y = (-1(x + 2))² - 5?

• Reflected over the x-axis, translated right 2 and down 5

• Reflected over the y-axis, translated right 2 and down 5

• Reflected over the x-axis, translated left 2 and down 5

• Reflected over the y-axis, translated left 2 and down 5

What mapping transforms y = x into y = 2(-x) +5?

• (x, y) →(-x, 2y + 5)

• (x, y) →(-2x, y + 5)

• (x, y) →(-x, 2y - 5)

• (x, y) →(-2x, y - 5)

What mapping transforms y = x³ into y = -(3x)³ - 7?

• (x, y) →(x÷3, -y + 7)

• (x, y) →(x÷3, -y - 7)

• (x, y) →(3x, -y - 7)

• (x, y) →(3x, -y + 7)

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

• (-2, 5)
• (-6, 5)
• (-4, 3)
• (-4, 7)

What are the transformations of this functions compared to the parent function y = √(x)?

• Horizontal translation 5, vertical translation -2, and reflected over the x-axis

• Reflected over the x-axis, vertical stretch 2, and horizontal translation 5

• Reflected over the x-axis, vertical stretch 2, and horizontal translation -5

• Horizontal translation 5, vertical translation -2

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal translation 1

• Vertical stretch by 2

• Horizontal stretch by 1/2