|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 x-axis, 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 Y1 = abs(X) thicker to distinguish it from the transformed graph.
Open the Y= editor and change the line style of Y1 = 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 Y1 and the corresponding points on Y2. 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 x-intercept 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.
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 x-Axis
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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