Function Transformations

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 original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?
(hint label a,b,c,d)

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

Tags

CCSS.HSF.BF.B.3

If the yellow curve has equation f(x)=x²,
(hint did it moved on the x or the y-axis)

• Then the blue curve is f(x) = x² - c
• Then the blue curve is f(x) = (x+c)²
• Then the blue curve is f(x) = (x-c)²
• Then the blue curve is f(x) = x²

 f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)
(hint did it became wider or narrow)

• g(x)=2f(x)
• g(x)=0.5f(x)
• g(x)=f(x) + 2
• g(x)=f(x + 2)

What is the transformation described?

• horizontal shift to the right 4 and vertical shift down 2
• horizontal shift to the left 4 and vertical shift up 2
• horizontal shift to the right 4 and vertical shift up 2
• horizontal shift to the left 4 and vertical shift down 2

Describe one of the transformations from
y = g(x)
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

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f
• The graph of f is a horizontal translation two units left of g
• The graph of g is a vertical stretch by a factor of 2 of the graph of f
• The graph of g is a reflection of the graph of f

If the blue graph is f(x)=|x|, then the red graph must be:
(hint what happened to the whole graph?)

• g(x)=|x+2|
• g(x)=|x|+2
• g(x)=|x-2|
• g(x)=|x|-2