Exploring Absolute Value

Exploring Absolute Value

• Absolute value is the distance from 0.
• The absolute value is always positive.
• Absolute value can be represented as |x|.
• It can be used to find the distance between two points on a number line.
• Absolute value can be transformed using A, C, and D values.

Absolute Value:

The absolute value represents the distance from 0. It is always positive and gives the magnitude of a number, regardless of its sign. For example, the absolute value of -5 is 5, and the absolute value of 7 is 7. It is denoted by |x|, where x is the number. The absolute value is useful in various mathematical operations and applications.

Exploring Absolute Value

• Reflect graph across the x-axis: -f(x) flips the graph
• Shifts: 2 to the left, 1 up, 3 to the left, 2 down
• General Form: y=a|x-h|+k
• Vertex Point: h is the x-coordinate
• Stretch/Compress: Makes Narrow or Wide

Graph Flipping

Trivia: When you apply the function -f(x) to a graph, it flips the graph across the x-axis. It's like looking at the graph in a mirror!

Exploring Absolute Value

The absolute value function, denoted as |x|, returns the distance of a number from zero on the number line. The vertex of the absolute value function is located at (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate. The axis of symmetry is the vertical line x = h. The slope of the line is represented by a. Rigid transformations can be applied to the absolute value function by adding or subtracting values inside the absolute value symbol. Reflections can be achieved by multiplying the function by -1. The parent function of absolute value is y = |x|.

Vertex of Absolute Value

The vertex of an absolute value function is represented as (h, k), where h is the x-coordinate and k is the y-coordinate. The vertex is the point where the graph of the function reaches its minimum or maximum value. It is the turning point of the V-shaped graph. In this case, the vertex is (h, k), which represents the coordinates of the lowest or highest point on the graph.

Exploring Absolute Value

• The absolute value function is represented by the equation y = |x|.
• The vertex of the absolute value function is the point (h, k).
• The parent equation of the absolute value function is f(x) = |x|.
• The domain of the absolute value function is (-∞, ∞).
• The range of the absolute value function is [0, ∞).