# Absolute Value Function

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In mathematics, the total value of a number is the distance of that number from 0 on the number line. The absolute value of a number is always positive or zero, and it is indicated by the symbol "| |". For instance, the absolute value of 3 is |3| = 3, and the absolute value of -3 is |-3| = 3.

An absolute value function is a function that takes a number as input and returns its absolute value as output. Absolute value functions are often written in form f(x) = |x|. For instance, the function f(x) = |x - 3| is an absolute value function that returns the absolute value of the difference between x and 3.

To write an absolute value function, you need to plan a series of points and then draw a smooth curve through those points.

## To graph an absolute value function follow the step-by-step guide here:

1. Write the function in form f(x) = |x - a|, where a is a constant.
2. Select a series of values for x and calculate the corresponding values for y. Absolute value functions are determined for all values of x, so you can select any set of x-values that you want. For each value of x, calculate the corresponding value of y using the formula y = |x - a|.
3. Determine the points on the graph. On the x-axis, plan the values of x that you chose in step 2. On the y-axis, plan the corresponding values of y.
4. Create a smooth curve through the points. Absolute value functions have a "V" shape, with the vertex (point of symmetry) at the value of x that makes the absolute value equal to zero. Connect the points with a smooth curve that follows the general shape of the function to draw the curve.