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 PRECALCULUS 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 xaxis (points with negative ycoordinates) are
reflected about the xaxis to above the xaxis.
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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 Fall '11
 Aytona
 Calculus, PreCalculus, 2 seconds, 1 seconds, 1.9 seconds, 5 Hertz

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