Absolute Value Concepts and Graphing

What is the absolute value?

What type of shape is an absolute value parent graph?

What is the parent function of absolute value?

What are the two different intervals in absolute value on a graph?

Where do the function intercept with the Y axis or X axis?

Example problem: y = |x-4| -2: What's the domain and range? Fill in the blank.

What is the Vertex of y = |x-4| -2?

With absolute value equations, do we graph one or both functions?

If the functions intersect (x & y), is there solutions?

If the equation is equal to a __________________ number, there is no solution.

In absolute value equations, we always solve for _____?

In absolute value equations, we always check what?

Example problem: 6= 2 |x-1| +2. What are the solutions?

Does the equation |3x+5| -2 = -1 have a solution? If not, why?

Can absolute value be on both sides of the equation and have solutions or just one side?

Key Concepts of Absolute Value

Absolute value denotes the distance of a number from zero on the number line.
The graph of an absolute value function has a distinctive V-shaped appearance, indicating increasing and decreasing intervals.

Parent Function and Graphing

The parent function of absolute value is represented by the equation y = |x|.
Absolute value graphs will exhibit two distinct intervals: one where the function is increasing and one where it is decreasing.

Intercepts and Vertex

Intercepts are the points where the graph crosses the X-axis or Y-axis.
For the function y = |x-4| - 2, the vertex is located at the point (4, -2).

Domain and Range

The domain of the absolute value function is all real numbers.
For the function y = |x-4| - 2, the range includes values of y that are greater than or equal to -2.

Graphing and Solutions

When graphing absolute value equations, both the positive and negative functions should be represented.
Solutions exist if the two functions intersect at points on the graph.
If an absolute value equation results in a negative number (e.g., |3x+5| - 2 = -1), it indicates no solution due to the nature of absolute values being non-negative.

Problem-Solving and Checking

Solve for x in absolute value equations, as the variable x is key to finding solutions.
It is crucial to verify the correctness of numbers in absolute value equations to ensure valid solutions.

Example Solutions

For the equation 6 = 2 |x-1| + 2, the solutions are x = 3 and x = -1.
Ensure all potential solutions are realistic and fit within the defined parameters of absolute value equations.

Explore key concepts of absolute value functions, including their distinctive V-shaped graphs. Understand the parent function, intercepts, domain, and range through various examples. This quiz will test your knowledge on graphing and analyzing absolute value equations.