• y = af(b(x - h)) + k
• "a" is vertical stretch
• "b" is horizontal stretch
• "h" is horizontal shift
• "k" is vertical shift
• when y = f(x) becomes y = af(b(x - h)) + k, (x, y) becomes ((1/b)x + h, ay + k)

Sketching the Graph of a Transformed Function Example #1

• use the equation to recognize the transformations y = af(b(x - h)) + k
• choose multiple points to transform, (x, y) becomes ((1/b)x + h, ay + k)
• plot new points and connect them

Sketching the Graph of a Transformed Function Example #2

Sketching the Graph of a Transformed Function Example #3

Sketching the Graph of a Transformed Function Example #4

Sketching the Graph of a Transformed Function Example #5

Sketching the Graph of a Transformed Function Example #6

Finding the Equation of a Transformed Function

• in y = af(b(x - h)) + k, find the value of "a", "b", "h", and "k"
• compare graphs to see if there has been any reflections (meaning "a" or "b" is negative)
• compare the width of one section on the original function with the width of the same section on the transformed function
  • b = new width/old width
• compare the height of one section on the original function with the height of the same section on the transformed function
  • a = new height/old height
• choose one point to transform using the horizontal and vertical stretches and reflections, find the shifts required to reach the transformed point
  • h = horizontal distance to point
  • k = vertical distance to point