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Name That Graph…. Parent Graphs or Base Graphs Linear Quadratic Absolute Value Square Root Cubic Exponential Math 30-11
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 30-12
3 1.1A Families of Functions Represents a horizontal translation h > 0, the translation is to the right h = 3, shift three units right h < 0, the translation is to the left h = -2, shift two units left With a horizontal translation, the domain may be affected, the range stays the same. y = f (x - h) y = f (x) h y = f (x + h) h Notice Replacement
Math 30-14 Consider the graph of y = f(x). Could f(x) be written as an equation? Yes, Piecewise function. Graph y = f(x + 1) Key Points Mapping (x, y) Domain of image in Interval Notation Range of image in Set Builder Notation (x-1, y) (-2, 0)(-3, 0) (-1, 3)(-2, 3) (2, 3)(1, 3) (5, 1) (4, 1) Horizontal shift one unit left Set Notation assumes Real Numbers
Write the equation of the function after a horizontal translation of 3 units left. Coordinates in Mapping Notation Math 30-15 Specific Function Notation Coordinates in Mapping Notation x is replaced by (x + 3) in function equation x is replaced by (x - 3) in ordered pair
Math 30-16 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 30-17 Write the equation of the transformed function, g(x). Horizontal shift two units right Replace x with (x – 2) in function equation Domain in Interval Notation: Original Image Mapping Notation:
Math 30-18 Page 12: 1c, 2b,c, 3a, 5a, 7, 12
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