1 5 b Combining Transformations Lets start with

1. 5 b Combining Transformations

Let’s start with a problem: Describe a basic graph and a sequence of transformations that can be used to produce a graph of the given function. 2 Starting with y = x , àDoes the order with which we apply these translate right 3 units, transformations matter? ? ? vertically stretch by 2, and translate down 4 units.

Combining Transformations Apply the following transformations, in order, to the graph of the squaring function. Graph the result. • a horizontal shift 2 units to the right • a vertical stretch by a factor of 3 • a vertical translation 5 units up Expand the final result!!!

Combining Transformations Apply the following transformations, in order, to the graph of the squaring function. Graph the result. • a horizontal shift 2 units to the right • a vertical stretch by a factor of 3 • a vertical translation 5 units up Now, apply the same transformations, but in the opposite order. Expand the final result!!! The Moral: Order often matters when stretches, shrinks, or reflections are involved…

More Practice Describe a basic graph and a sequence of transformations that can be used to produce a graph of the given function. 3 Starting with y = x , horizontally shrink by 1/3 and translate up 2 units.

More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x).

More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A vertical stretch by a factor of 2

More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A horizontal translation 1 unit to the left

More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A vertical translation 3 units down

White board… Describe the translations to vertical shrink of ¼ horizontal shrink of 1/3, shift down 4 shift 2 left, reflection across yaxis, horizontal shrink of ¼, vertical shrink of ½, shift 3 up Homework: p. 140 29, 31, 35 -49 Quiz tomorrow sections 1. 4 -1. 5!