Parent Functions and Transformations

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

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

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

• Vertical translation up by 2 units.

• Horizontal compression by a factor of 1/2

How did the equation shift from the parent function? y = f(x - 4) (a)  

• Shift right by 4
• Shift left by 4
• Horizontal Stretch by 4
• Vertical Stretch by 4
• Shift down by 4

How did the equation f(x) = x change if

g(x) = 1/2f(x) + 11

• Vertical stretch and shift up 11

• Horizontal shrink and shift down 11

• Vertical shrink and shift up 11

• Horizontal stretch and shift down 11

How did the equation shift from the parent function? y = -3f(x) + 5

• Reflection over x-axis, steeper, up 5

• Reflection over y-axis, less steep, right 5

• Steeper, left 5

• reflection over x-axis, less steep, up 5

How did the equation shift from the parent function? y = f(x + 7) (a)  

• Up 7
• Down 7
• Left 7
• Right 7

Match the following linear transformations.

• Horizontal compression

  Shifts right 2

  Shifts down 3

• 
• Horizontal compression

  Shifts right 1

• 
• Reflection

  Shifts left 1

• 
• Vertical stretch

  Shifts right 2

  Shifts up 3

• 
• Reflection

  Shifts right 1

• 

The graphs of linear functions f and g are shown on the grid.

Which function is best represented by the graph of g?

Find the slope

• -5/3
• -3/5
• 5/3
• 3/5

What is the equation of this graph?

• f(x) = (x -5)² + 1
• f(x) = (x - 1)² - 5
• f(x) = (x + 1)² - 5
• f(x) = (x + 5)² +1