• y = f(x) becomes y = af(b(x - h)) + k
  • plug in "b(x - h)" in for x
  • multiply "a" at the front, and add "k" to the end
• y = c^x becomes y = a*c^(b(x - h)) + k
  • calculate c^(b(x - h)) first, then multiply by "a", finally add "k"
• (x, y) becomes ((1/b)x + h, ay + k)

How the Horizontal Asymptote Changes After Transformation

• the new asymptote is the "k" value in y = a*c^(b(x - h)) + k

Finding the Y-Intercept of a Transformed Function

• the y-intercept is where x = 0, so plug in 0 for x, and solve for y

Transforming Exponential Functions Example #1

• y = 2(0.25^(x - 3)) - 2

Transforming Exponential Functions Example #2

• y = -2^(-3x) + 5
• note that this actually represents y = -(2^(-3x)) + 5, because remember the base of the exponent ("c") cannot be negative

Transforming Exponential Functions Example #3

• y = 3(0.25^(0.5(x + 3))) - 1