Horizontal Translations Name That Graph Parent Graphs or
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Horizontal Translations Name That Graph…. Parent Graphs or Base Graphs Linear Absolute Value Cubic Quadratic Square Root Exponential Math 30 -1 1
Identify the function equation that is different from the rest. In mathematics, transformations refer to a manipulation of the graph of a function or relation such as a translation, a reflection or a stretch. The result of a transformation can be called the image graph or image function. A transformation is indicated in a function equation by including a parameter in the parent function. Math 30 -1 2
1. 1 A Families of Functions Represents a horizontal translation h > 0, the translation is to the right h < 0, the translation is to the left h = 3, shift three units right h = -2, shift two units left Notice Replacement y = f (x) h y = f (x - h) y = f (x + h) h With a horizontal translation, the domain may be affected, Math 30 -1 the range stays the same. 3
Consider the graph of y = f(x). Could f(x) be written as an equation? Yes, Piecewise function. Graph y = f(x + 1) Horizontal shift one unit left Key Points Mapping (x, y) (x-1, y) (-2, 0) (-3, 0) (-1, 3) (-2, 3) (1, 3) (5, 1) (4, 1) Domain of image in Interval Notation Range of image in Set Builder Notation Set Notation assumes Real Numbers Math 30 -1 4
Write the equation of the function after a horizontal translation of 3 units left. x is replaced by (x + 3) in function equation Function Notation Specific Coordinates in Mapping Notation x is replaced by (x - 3) in ordered pair Math 30 -1 5
Given Write the equation of the function after a horizontal translation of 4 units to the right. x is replaced by (x – 4) in the function equation Math 30 -1 6
Write the equation of the transformed function, g(x). Horizontal shift two units right Replace x with (x – 2) in function equation Mapping Notation: Domain in Interval Notation: Original Image Math 30 -1 7
Assignment: Page 12: 1 c, 2 b, c, 3 a, 5 a, 7, 12 Math 30 -1 8
