## What is an Absolute Value?

The absolute value of a number is the value of the number without its sign. So, the absolute value of 5 is 5, and the absolute value of -5 is also 5. The absolute value of a number can be thought of as the distance of the number from 0 on a number line.

### The definition of an absolute value

A number’s absolute value is the distance from zero on a number line. Basically, it is the number’s magnitude. The absolute value of a number is always positive (or zero). So, if you have a negative number, the absolute value will make it positive. For example, the absolute value of -5 is 5 because 5 units away from 0 on a number line. The symbol for absolute value is two vertical bars side by side: ||

### An example of an absolute value

The absolute value of a number is the distance of that number from zero on a number line. The absolute value of a number is always positive or zero. It is written with the absolute value bars around the number like this: |4| = 4

Here are some more examples of absolute value:

5 = |5| because 5 is 5 units to the right of zero

-5 = |-5| because -5 is 5 units to the left of zero

|-4| = 4 because -4 is 4 units to the left of zero

## What is a y x graph?

y x graph is a line graph that is used to determine the absolute value of a number. It is also used to find out the roots of a polynomial equation.

### The definition of a y x graph

A y x graph, also called a coordinate graph or Cartesian coordinate system, is a two-dimensional graph that specifies each point uniquely in a plane by its coordinates. The coordinates are numbers that determine the position of a point on the graph. Each point on the graph is represented by an ordered pair of numbers, called coordinates, which are written as (x, y).

### An example of a y x graph

A y x graph is a visual representation of data that shows the relationship between two variables. In mathematics, a graph is a collection of points, called vertices, and the lines connecting them, called edges.

In a y x graph, the x-axis represents the independent variable, while the y-axis represents the dependent variable. The point where the two axes intersect is called the origin. The independent variable is usually plotted on the x-axis, while the dependent variable is plotted on the y-axis.

The most common type of y x graph is a Cartesian coordinate system, which uses two perpendicular axes (x and y) to create a quadrant system. In a Cartesian coordinate system, each vertex is represented by a pair of coordinates (x,y). The x-coordinate represents the horizontal position of the vertex, while the y-coordinate represents its vertical position.

The distance between any two points can be found by using the Pythagorean theorem. In a Cartesian coordinate system, this theorem states that:

d = √( (x2 – x1)2 + (y2 – y1)2 )

where d is the distance between points (x1,y1) and (x2,y2).

## How to graph the absolute value of a function

### The steps to graph the absolute value of a function

To graph the absolute value of a function, you will need to take the following steps:

- First, identify the function’s vertex. This is the point where the function changes from positive to negative, or vice versa.
- Next, plot the vertex on a graph.
- Then, draw a line segment from the vertex to each point on either side of it. These line segments will be perpendicular to the x-axis.
- Finally, extend these line segments until they intersect the x-axis.

An example of graphing the absolute value of a function

To graph the absolute value of a function, you need to find the x and y intercepts. The x intercept is where the line crosses the x-axis, and the y intercept is where the line crosses the y-axis. To find these points, you need to set y=0 and solve for x. This will give you the x intercept. To find the y intercept, set x=0 and solve for y. This will give you the y intercept.

Once you have these points, you can start graphing. To graph a line, you need to start at one of the points and then plot additional points that are equidistant from each other. For example, if you’re graphing a line on a graph paper with 1 inch squares, each point should be 1 inch away from the previous point.

When graphing the absolute value of a function, it’s important to remember that the absolute value can never be negative. This means that your line will always either be horizontal or vertical. If your line is horizontal, it will cross the x-axis at your x intercept and then continue parallel to the x-axis. If your line is vertical, it will cross the y-axis at your y intercept and then continue parallel to the y-axis.