Discover The Absolute Value Function: Its Definition, Graph, And Application

f(x)=|x|

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The function f(x) = |x| is an absolute value function. It returns the distance of the input x from the origin (0) on the number line. The absolute value of a number can never be negative because it measures the distance of a number from zero.

For example, if we plug in x = -3 into the function f(x) = |x|, we get f(-3) = |-3| = 3. This means that -3 is three units away from 0 on the number line. Similarly, if we plug in x = 5, we get f(5) = |5| = 5, which means that 5 is five units away from zero on the number line.

The graph of the absolute value function is a V-shaped graph with the vertex at (0, 0). The right side of the V is the positive side of the x-axis, and the left side of the V is the negative side of the x-axis.

To sketch the graph of the absolute value function, we can first plot the vertex at (0, 0). Then we can choose a few x-values, such as x = -2, -1, 0, 1, and 2, and find their corresponding y-values by taking the absolute value of each x-value. Finally, we can plot these points and connect them with a V-shape. The resulting graph will be the graph of the absolute value function f(x) = |x|.

In summary, the absolute value function f(x) = |x| measures the distance of the input x from zero on the number line. Its graph is a V-shaped graph with the vertex at (0, 0).

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