Module 3  Functions and Transformations 
Introduction  Lesson 1  Lesson 2  Lesson 3  Lesson 4  Self Test 
Lesson 3.1: Stretches and Reflections 
In this lesson you will begin with the graph of the absolute value function, , and then explore how to stretch and shrink the graph vertically, reflect the graph across the xaxis, and shift the graph vertically and horizontally. Stretches, shifts and reflections of a graph are called transformations. The Absolute Value Function Begin the exploration of transformations of graphs by displaying the graph of the absolute value function, .
Stretch and Shrink Vertically Explore the effect of multiplying the absolute value function by 2 and compare it with the basic absolute value graph. Make the graph of Y_{1} = abs(X) thicker to distinguish it from the transformed graph. Open the Y= editor and change the line style of Y_{1} = abs(X) to thick.
View the table of values for the two functions.
Notice that each Y2 value is 2 times the corresponding Y1 value.
The Stretch Factor The table below shows points on the graph of Y_{1} and the corresponding points on Y_{2}. The illustration shows the relative position of corresponding points. The graph of is a vertical stretch of the graph of and the stretch factor is 2. Notice that the xintercept is not stretched because 2(0) = 0. 3.1.1 Graph and in a Zoom Standard window and describe the resulting transformations. Click here for the answer. Reflections Another interesting transformation is a reflection, which is a mirror image. The reflection of a point across a line sends the point p onto the point q, where the reflecting line is the perpendicular bisector of the line segment between p and q. Reflecting a graph across a line reflects each point of the graph across the line. Reflecting Across the xAxis Explore the effect of multiplying a function by 1.
Each Y2 value is the negative of the corresponding Y1 value. 3.1.2 Graph and in a Zoom Standard window and describe the transformation. Click here for the answer. 
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