Transformation of Functions Notation

Describe the transformation that occurred

p(x) = f(x + 3)

• Right 3 units

• Vertical Stretch

• Up 3 units

• Left 3 units

Describe the transformation that occurred.

h(x) = f(x) + 2

• up 2 units

• left 2 units

• Vertical Strech

• right 2 units

Describe the transformation that occurred

g(x) =2f(x)

• Up 2 units

• vertical compression

• vertical stretch

• Right 2 Units

Describe the transformation of y = f(x) for the new function
 y = 1/5f(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 = 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

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 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

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)
• f(-x)
• f^-1(x)
• f(2x)

  The blue function is the parent function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³