2.6 Transformations of Parent Functions

Match the following:

• 
• Square Root Parent

• f(x)= x

• Linear Parent

• Rational Parent

• Quadratic Parent

• 

• Vertical Stretch
• Horizontal Translation Right
• Vertical Translation Down
• Refection across the x-axis
• Reflection across the y-axis
• Vertical Translation Up
• Horitzontontal Translation Left
• Vertical Compression
• Horizontal Stretch

• Horizontal Translation Left
• Vertical Compression
• Refection across the x-axis
• Reflection across the y-axis
• Vertical Translation Up
• Horizontal Stretch

What is the equation of the parent function shown in the graph?

Mathematical Equivalence

ON

Transform the quadratic parent function to show that there is a vertical translation up 4 units, a horizontal translation left 2 units, and vertical reflection.

(Make sure one of the points is on the vertex, and the other a zero.)

• Shift up 3 units

• Shift down 3 units

• Reflection over the y-axis

• Reflection over the x-axis

• Reflection over the x-axis

• Translation 4 units left

• Translation 4 units up

• Translation 3 units left

• Translation 3 units down

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

• y = x² + 2
• y = -x² + 2
• y = x² - 2
• y = -(x + 2)²

• y = Ix + 2I - 1
• y = -Ix + 2I - 1
• y = -Ix - 2I - 1
• y = -Ix + 1I - 2

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

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