**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!