Unit 5 – Linear Functions

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Presentation transcript:

Unit 5 – Linear Functions Topic: Linear Transformations

The Linear Parent Function The most basic function in the family of all linear functions. Linear Parent Function Equation All linear functions are transformations of the linear parent function.

What is a transformation? A change of position in the coordinate plane. 3 types of linear transformations. Translation Rotation Reflection

Translation A slide in the position of the graph. Translating a linear function shifts the line up or down on the y-axis. g(x) is a vertical translation 5 units down from the linear parent function f(x). h(x) is a vertical translation 3 units up.

Rotation A transformation about a point. Rotating a linear function changes the steepness of the line. g(x) is a rotation of the linear parent function towards the y-axis. h(x) is a rotation towards the x- axis

Reflection Producing a mirror image over an axis. Reflecting a linear function “flips” the line over the y- axis. g(x) is a reflection of the linear parent function across the y-axis.

Multiple transformations From the linear parent function f(x), g(x) is reflected, translated up 4 units, and rotated towards the x-axis.

Journal Entry Describe how you would change the value of m and/or b to accomplish the following: A translation A rotation towards the x-axis A rotation towards the y-axis A reflection across the y-axis

Homework Textbook Section 5-9 (pg. 361): 20-28, 35-38 Due 11/28 (2A) or 11/29 (2B)