PREC11 Unit6 notes

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Unformatted text preview: = | 2x − 3 | by transforming the graph of the linear function and then verify your graph by writing the absolute value function as a piecewise function. o Draw the graph of y = 2x − 3 . Use a dashed line; part of this graph is not used for the absolute value function’s graph. y 2 o The points on the x-axis and the points above the x-axis are invariant points; they will also be on the graph of the absolute value function. Draw these points with a -2 0 2 x -2 solid line. o The points below the x-axis will be affected by the transformation; they will be reflected about the x-axis to above the x-axis. if 2x − 3 o | 2x − 3 | = 0 if − (2 x − 3) if so y = | 2x − 3 | becomes y= Unit 6: Day 2 notes - Absolute Value Functions Page 3 of 4 GRAPHING y = | a(x − p)2 + q | , THE ABSOLUTE VALUE OF A QUADRATIC FUNCTION example: Draw the graph of y = | x2 − 4x + 3 | by transforming the graph of the quadratic function and then verify your graph by writing the absolute value function as a piecewise function. o Draw the graph of It's vertex equation is The vertex is (2,−1) y = x2 − 4x + 3 y y = (x − 2)2 − 1 6 It's factored form is y = (x − 1)(x − 3) The x-intercepts are (1,0) and (3,0) 4 2 Use a dashed line. o The points on and above the x-axis are invariant points. Draw these points with a solid line. 0 2 x 4 o Reflect the points below the x-axis to above the x-axis. ( x − 2)2 − 1 if ( x − 1)( x − 3) > 0 o | x2 − 4x + 3 | = 0 if ( x − 1)( x − 3) = 0 ( x − 2)2 − 1 if ( x − 1)( x − 3) < 0 − ( x − 2)2 − 1 if x ≤ 1 or x ≥ 3 2 so y = | x − 4x + 3 | becomes y = 2 − ( x − 2) + 1 if 1 < x < 3 exercise: Draw the graph of y = | x2 − 4 | by transforming the graph of the quadratic function. Then verify your graph by writing the absolute value function as a piecewise function. y 3 -3 0 -3 3 x Unit 6: Day 2 notes - Absolute Value Functions Page 4 of 4 exercise: Draw the graph of y = | x2 + 1 | by transforming the graph of the quadratic function. y 3 -3 0 x 3 -3 2 [Answer: same as the graph of y = x + 1] exercise: Draw the graph of y = | −x2 − 1 | by transforming the graph of the quadratic function. y 3 -3 0 x 3 -3 2 [Answer: same as the graph of y = x + 1] y EXTENSION Graph y= | f (x) | 2 if x > 2 for f (x) = x if − 2 ≤ x ≤ 2 −2 if x <...
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This document was uploaded on 02/16/2014 for the course MATH Pre-Calcul at Holy Cross Regional High School.

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