Transformations of Functions

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a translation shifting f(x) 4 units up
• a translation shifting f(x) 4 units down
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Vertical Compression by a factor of 2
• Vertical Stretch by a factor of 2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x² is replaced with 1/2⋅f(x)?

• Vertical Compression by a factor of 1/2
• Vertical Stretch by a factor of 1/2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units
• Narrower
• Vertical translation up by 2 units.
• Reflection across the x-axis.

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

• The graph of y = f(x) compressed horizontally by a factor of 1/5
• The graph of y = f(x) was stretched horizontally by a factor of 5
• The graph of y = f(x) was compressed vertically by a factor of 1/5
• The graph of y = f(x) was stretched vertically by a factor of 5

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

• The graph of y = f(x) was flipped vertically across the x axis. 
• The graph of y = f(x) was flipped horizontally across the y axis.
• The graph of y = f(x) was shifted down.
• The graph of y = f(x) was shifted up

Tags

CCSS.HSF.BF.B.3

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

• The graph of y = f(x) was flipped vertically across the x axis. 
• The graph of y = f(x) was flipped horizontally across the y axis.
• The graph of y = f(x) was shifted down.
• The graph of y = f(x) was shifted up

Tags

CCSS.HSF.BF.B.3

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

• Shifted up 5 units
  Shifted right 3 units
  Stretched vertically by a factor of 3
• Shifted up 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 3
• Shifted down 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 3
• Shifted down 5 units
  Shifted left 3 units
  Stretched vertically by a factor of 1/3

Identify the transformation from the graph of f(x)=x² to the graph g(x)= x² - 5

• shifted up five units
• shifted down five units
• shifted left five units
• shifted right five units

Which equation describes the transformation of shifting f(x)=x³ four units down?

• x³+ 4
• x³- 4
• (x - 4)³
• (x + 4)³

Tags

CCSS.HSF.BF.B.3