PREC11 Unit6 notes

Does x y equal x y for all values for x and y

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Unformatted text preview: 7) ? b) | −5 | • | 7 | c) Does | (−5)(7) | equal | (−5) | • | (7) | ? Does | x y | equal | x | • | y | for all values for x and y ? Therefore: x2 = x when x ≥ 0 and x 2 = −x when x < 0 |x| Recall: − | (5)(7) | =x when x ≥ 0 and |x| when x < 0 x2 = |x| = −x PRE-CALCULUS 11 Unit 6 – Day 2: ABSOLUTE VALUE FUNCTIONS ABSOLUTE VALUE FUNCTIONS An absolute value function is a function that includes an absolute value of a variable expression. The basic absolute value function is y = | x | . We will be drawing the graph of functions that are the absolute value of linear functions or the absolute value of quadratic functions by transforming the graph of the linear or quadratic function’s graph. GRAPHING y = | mx + b | , THE ABSOLUTE VALUE OF A LINEAR FUNCTION example: Draw the graph of y = | x + 2 | by transforming the graph of y = x + 2 . x −5 −4 −3 −2 −1 0 1 x+2 −3 −2 −1 0 1 2 3 x −5 −4 −3 −2 −1 0 1 |x + 2| y =y =y 3 2 1 0 1 2 3 (−5,−3) (−4,−2) (−3,−1) (−2,0) (−1,1) (0,2) (1,3) 2 -4 -2 2 x 2 x -2 y=x+2 y = | x + 2| (−5,3) (−4,2) (−3,1) (−2,0) (−1,1) (0,2) (1,3) 0 y 2 -4 -2 0 -2 When absolute value is applied to a function, the original function's graph is transformed - all points below the x-axis (points with negative y-coordinates) are reflected about the x-axis to above the x-axis. Points that remain unchanged during a transformation are called invariant points. Unit 6: Day 2 notes - Absolute Value Functions Page 2 of 4 If we apply the mathematic definition of absolute value, y = | x + 2 | can be written as if x + 2 > 0 x+2 y= 0 if x + 2 = 0 − ( x + 2) if x + 2 < 0 which simplifies to x + 2 if x ≥ −2 y= − x − 2 if x < −2 Does this equation describe the graph drawn? A function written in this format is said to be in piecewise notation. Remember to consider characteristics of graphs we have seen before; the domain and range, the vertex, the axis of symmetry exercise: Draw the graph of y...
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