Transformation of Quadratics Using 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.

g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).

• f(x) has been translated to the left one and down five.
• f(x) has been translated to the right one and down five.
• f(x) has been translated to the left one and up five.
• f(x) has been translated to the right one and up five.

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

Which describes the transformation of 
f(x) = x² to the graph of g(x) = -x²?

• reflection across x-axis
• reflection across y-axis
• vertical compression
• horizontal compression

Which describes the transformation of

f(x) = x² to the graph of g(x) = 4x²?

• vertical stretch

• horizontal stretch

• vertical compression

• horizontal compression

Transformations are horizontal if they are....

• inside parenthesis
• outside parenthesis
• there are no parenthesis

Transformations are vertical if they are...

• inside parenthesis
• outside parenthesis

Which describes the transformation of

f(x) = x² to the graph of g(x) = -4x²?

• vertical stretch

• horizontal stretch

• vertical compression

• horizontal compression

• reflection about the x-axis