6 Transformations of Graphs Throughout this section we consider the relationship So the graph of the new function f(−x) is the reflection of the

Using transformations, many other functions can be obtained from these parents functions of and translated 4 units up and 6 units to the left

Chapter 6: Transformations of Functions Their Graphs 6 1 6 2 – TRANSLATIONS REFLECTIONS Objectives: • identify the effect on the graph of a function

The Fundamental Graphing Principle for Functions says that for a point (a, 6 7 y = f(x) shift up 2 units ------------→ add 2 to each y-coordinate

Lecture 1 3a, Transformations of Functions: Shifts Dr Ken W Smith Smith (SHSU) Elementary Functions 2013 6 / 35 Horizontal shifts

f(x) Page 4 Math 150 – c Lynch 5 3–Transformation of Functions 4 of 6 Example 6 Apply the appropriate transformations to the graphs of basic functions to

2 fév 2018 · Use the Explore: Transformations resource to investigate graphs of the cuts the x-axis at (1, 0) and (-1, 0) and the y-axis at (0, -6)

Exercise 1: Compare the graph of the function y = | + 3| and y = | − 2| to the graph of Algebra 2: 6-1 Transformation of Absolute Value Functions

24 fév 2018 · Parent Functions and Transformations Transformation of Functions Example of function that is shifted down 4 units and right 6 units

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A parent function is the most basic version of an algebraic function Types of Parent Functions Linear f(x) = mx + b; Quadratic f(x) = x2

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You can transform piecewise functions by applying transformations to each piece independently Recall the rules for transforming functions given in the table

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Each function in the family is a transformation of the parent function Ex 6 Given the following table, find f(-x) and –f(x) and sketch

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Learning Target: I can analyze and describe transformations of functions Example of function that is shifted down 4 units and right 6 units from the

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Graph each transformation of the parent function and describe the change from the original y = x2; Left 5/3, Up 7/12, Vertical stretch of 4/3 6

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Moving the function 6 units to the left corresponds to a horizontal translation by -6 units Moving 8 units down corresponds to vertical translation by -8 units

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Transformations to Parent Functions Translation (Shift) A vertical translation is made on a function by adding or subtracting a number to the function

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Transformations of the six basic functions Directions: Write the equation for each graph below Write the correct equation based on the description below

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Graph the function and its parent function then describe the transformation

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