Absolute Value Function
This is an absolute value function: (x) = |X|
It is also sometimes written: abs(x)
This is its graph:
It is also sometimes written: abs(x)
This is its graph:
It takes a right angle at (0,0)
It's an even function.
Its Domain is all Real Numbers.
Its Range is the Non-Negative Real Numbers: [0, +∞)
Absolute Value Standard form Equation:
y=|x−h|+k
For vertex:
h = x
k = y
Translations:
the shifting of a graph vertically, horizontally, or both
horizontal shift = left/right shift
vertical shift = up/down shift
diagonal shift = a combination of horizontal and vertical shifts
A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor, k. The value of k determines whether the dilation is an enlargement or a reduction.
If |k| > 1, the dilation is an enlargement.
If |k| < 1, the dilation is a reduction.
A reflection is like a mirror image. The line of reflection acts as the mirror and is halfway between the point and its image. If the point is its own reflection, then it is a point on the line of reflection.
Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halve.
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “U”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “U”-shape.
the shifting of a graph vertically, horizontally, or both
horizontal shift = left/right shift
vertical shift = up/down shift
diagonal shift = a combination of horizontal and vertical shifts
A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor, k. The value of k determines whether the dilation is an enlargement or a reduction.
If |k| > 1, the dilation is an enlargement.
If |k| < 1, the dilation is a reduction.
A reflection is like a mirror image. The line of reflection acts as the mirror and is halfway between the point and its image. If the point is its own reflection, then it is a point on the line of reflection.
Every parabola has an axis of symmetry which is the line that runs down its 'center'. This line divides the graph into two perfect halve.
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “U”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “U”-shape.