f(x) = |x|
The function f(x) = |x| represents the absolute value of x
The function f(x) = |x| represents the absolute value of x. The absolute value of a number is the distance of that number from zero on the number line. It is denoted by two vertical bars surrounding the number or expression.
For example, if x = 5, then f(5) would be |5|, which is equal to 5 because 5 is 5 units away from zero on the number line. Similarly, if x = -3, then f(-3) would be |-3|, which is also equal to 3 because -3 is 3 units away from zero on the number line.
The absolute value function is symmetric with respect to the x-axis, meaning that the values of f(x) with positive and negative x-values are the same. This is because the distance from zero is the same regardless of whether the number is positive or negative.
To graph the function f(x) = |x|, you would plot points that represent the absolute value of various x-values. For x-values greater than or equal to zero, the function will be equal to x itself (since the distance from zero for positive numbers is x). For x-values less than zero, the function will be equal to -x (since the distance from zero for negative numbers is -x). This will give you a V-shaped graph, also known as an absolute value graph.
I hope this clarifies the concept of the absolute value function! Let me know if you have any further questions.
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