Transformations of Functions

Which of the following transformations are present (select all that apply)?

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

• reflection over horizontal axis

• reflection over vertical axis

• horizontal compression

• vertical shift

• Rotation about origin

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

• Reflect over y-axis
  Shifted down 10 units
  Shifted left 6 units

• Reflect over x-axis
  Shifted up 10 units
  Shifted left 6 units

• Reflect over y-axis
  Shifted up 10 units
  Shifted right 6 units

• Reflect over x-axis
  Shifted down 10 units
  Shifted left 6 units

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5

• Right 3 and down 5

• Left 3 and down 5

• Right 3 and up 5

The graph of g(x) is a
(a)   translation ​ (b)   units ​ ​ (c)   the graph.

• vertical

• 2

• 1

• up

• down

• left

• right

The graph of r(x) is a​ ​ (a)   ​by the graph of f(x) by a factor of ​ ​ (b)   .

• horizontal stretch

• horizontal shrink

• vertical stretch

• vertical shrink

• 1/3

• 3

• 2/3

Take the specified parent function and translate it left by 7 units, reflect it vertically, stretch it vertically by a factor of 2 units, then translate it 2 units up.

Mathematical Equivalence

ON

The image shows a ​ (a)   translation ​ (b)   units ​ (c)  

• horizontal

• 4

• left

• vertical

• right

• 3

• up

Given the following, translate the graph seven left and two up!

Mathematical Equivalence

ON

Take the specified parent function and translate it left by 7 units, reflect it vertically, stretch it vertically by a factor of 2 units, then translate it 2 units up.

Mathematical Equivalence

ON