f(x)=|x|
The function you have provided is f(x) = |x|
The function you have provided is f(x) = |x|. This is known as the absolute value function.
The absolute value of a number is the distance of that number from zero on the number line. So, when applied to a variable, like in this case x, the absolute value function gives the distance of x from zero.
Let’s break down how this function works:
– For positive numbers: if x is positive, the absolute value of x is equal to x itself. So, f(x) = x. For example, if x = 3, then f(x) = |3| = 3.
– For negative numbers: if x is negative, the absolute value of x is equal to its opposite. So, f(x) = -x. For example, if x = -3, then f(x) = |-3| = 3.
– For zero: the absolute value of zero is zero. So, f(x) = 0 when x is zero.
To graph the function f(x) = |x|, you would plot points on a coordinate plane based on the value of x and its corresponding absolute value (y). The resulting graph is a V-shaped curve, known as the “absolute value graph”. It opens upward from the point (0, 0) on the coordinate plane.
Overall, the absolute value function is a helpful tool in manipulating and understanding the distance of values from zero.
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