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Absolute Value Equations

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Wyatt Coggins

on 3 June 2016

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Transcript of Absolute Value Equations

Absolute Value Equations
What about transformations?
Transformation- A general term for four specific ways to manipulate the shape of a point, a line, or shape.
Whats up with 0's and intercepts?
Zero- the points where the graph of the equation crosses the x-axis. (aka x-intercepts)
Y-intercept- where the line crosses the y-axis.
f(x)=-|x|
f(x)= |x|
f(x)=|x|
Finally: D+R & I+D
Domain & Range: the set of all input (D), and output (R) values
Interval: the set of x-values for which the cooresponding y-values are increasing/decreasing
And Now
End Behavior & Symmetry
End Behavior- the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
Symmetry- axis of symmetry of a graph is a vertical line that divides the function into two congruent halves.
Hallie, Tim, Wyatt, and Jacob
What is absolute value?
Absolute Value- the magnitude of a real number without regard to its sign.
y = a|x-h|+k

Parent Function: f(x)= |x|
Domain: ☻♠(-∞,╠ ∞↨)
Range: [0, ∞↨)
Zeros: {0}
Y-intercept: {0}
Ex: f(x)= -|x|
or
f(x)=|x-2|
or
f(x)=|x|+4
Domain: (-∞,∞)
Range: (-∞,0]
Zeros: {0}
Y-intercept: {0}
f(x)=|x-2|
Domain: (-∞,∞)
Range: [0,∞)
Zeros: {2}
Y-intercept: {2}
Ex: f(x)= |x+3|-2
f(x)=|x+3|-2
Domain: (-∞,∞)
Range: [-2,∞)
Zeros: {-5,-1}
Y-intercept: {1}
Ex:
f(x)=|x|
f(x)=|x|
Domain: ☻♠(-∞,╠ ∞↨)
Range: [0, ∞↨)
Zeros: {0}
Y-intercept: {0}
Ex: f(x)=|x|
Domain: ☻♠(-∞,╠ ∞↨)
Range: [0, ∞↨)
Interval I: (0,∞)
Interval D: (-∞,0)
f(x)=|x|+4
Domain: (-∞,∞)
Range: [4,∞)
Zeros: None
Y-intercept: {4}
That's All Folks!
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