Absolute Value of a Function
y = f(x) = |f(x)| where f(x) is positive, where f(x) is negative |f(x)| is reflected across the x – axis.
The absolute value function is a mathematical function that returns the non-negative value of a given quantity, ignoring its sign. It can be represented by the symbol “|x|” and is read as “the absolute value of x.” The absolute value of a number can be found by disregarding its positive or negative character and only considering its numerical value.
The absolute value function can also be applied to more complex functions. To find the absolute value of a function, you simply apply the absolute value function to the output of the given function. For example, if we have a function f(x), the absolute value function lets us find the absolute value of f(x) as |f(x)|.
To graph the absolute value function, we start by plotting a point at (0, 0). Then, we plot another point for each value of x where the function changes signs. For example, since the absolute value of -3 and 3 is the same (3), we plot a point at (-3, 3) and at (3, 3). We then connect these points with a straight line, creating a “V” shape. This shape is the graph of the absolute value function.
In summary, the absolute value function is a mathematical function that returns the non-negative value of a given quantity, ignoring its sign. It can be applied to complex functions to find the absolute value of their outputs. The graph of the absolute value function is a “V” shape, with a point at (0, 0) and additional points plotted where the function changes signs.
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