Transformation Function Notation

Describe the transformation of y = f(x) for the new function
 y = f(x) - 5

• The graph of y = f(x) was shifted to the right 5 units. 

• The graph of y = f(x) was shifted to the left 5 units. 

• The graph of y = f(x) was shifted up 5 units. 

• The graph of y = f(x) was shifted down 5 units.

What does the transformation f(x)↦5f(x) do to the graph of f(x)?

• Stretches it vertically

• moves down

• moves up

• compresses it vertically

Let f(x) = x². If f(x) is vertically compressed, let g(x) be the result of the transformation of f(x).

g(x) could be expressed as ...

• 5f(x)

• f(x) + 5

• 0.333f(x)

• f(x + 5)

Which describes the transformation of f(x) = x² to the graph of g(x) = ¹/₄x²?

• vertical stretch

• horizontal stretch

• vertical compression

• horizontal compression

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

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

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

• Left 3 up 5

• Right 3 down 5

• Left 3 down 5

• Right 3 up 5

Rewrite g(x) in translation form g(x) = f(x) + k

​ (a)   ​ ​ (b)   ​ (c)   ​

• g(x)=

• f(x)

• -11

• 7

• 9

• +11

• f(x)=