Lesson 1

Remember that when you sketch a graph, you must apply the transformations in the order of stretches and reflections before translations.

In Try This 4 you may have found that the parameters a, b, h, and k change the graph of an exponential function in the form f(x) = a(c)b(x–h) + k in the ways summarized in the following chart. Note: You may find it helpful to look at Multiple Transformations from Try This 4 as you review this chart.

Parameter	Transformation	Example
a	vertical stretch by a factor of |a| about the x-axis when a < 0, reflection in the x-axis mapping notation: (x, y) → (x, ay)
b	horizontal stretch by a factor of  about the y-axis when b < 0, reflection in the y-axis mapping notation:
h	horizontal translation of h units left or right mapping notation: (x, y) → (x + h, y)
k	vertical translation of k units up or down mapping notation: (x, y) → (x, y + k)