absolute value parent function
The absolute value parent function, also known as the absolute value function, is a special type of function in mathematics
The absolute value parent function, also known as the absolute value function, is a special type of function in mathematics. It is denoted by f(x) = |x|, where “x” represents the input value and “|x|” denotes the absolute value of x.
The absolute value of a number is defined as the distance of that number from zero on the number line, regardless of the direction. In other words, it gives the “absolute” magnitude or size of a number.
The absolute value parent function, f(x) = |x|, can be graphed as a “V”-shaped curve called a “V-curve” or “V-graph”. This curve is symmetric with respect to the y-axis, meaning that the left and right sides of the graph are mirror images of each other.
The graph of the absolute value function passes through the origin (0, 0) on the coordinate plane because |0| = 0. As you move to the right of the origin, the graph follows a linear upward path with a slope of 1. Likewise, as you move to the left of the origin, the graph follows the same linear upward path but reflected across the y-axis.
To demonstrate this, let’s plot a few points on the graph of the absolute value function:
For x = -3, f(-3) = |-3| = 3, so we have the point (-3, 3).
For x = -2, f(-2) = |-2| = 2, so we have the point (-2, 2).
For x = -1, f(-1) = |-1| = 1, so we have the point (-1, 1).
For x = 0, f(0) = |0| = 0, so we have the point (0, 0).
For x = 1, f(1) = |1| = 1, so we have the point (1, 1).
For x = 2, f(2) = |2| = 2, so we have the point (2, 2).
For x = 3, f(3) = |3| = 3, so we have the point (3, 3).
Plotting these points on the coordinate grid and connecting them will give you the V-shaped graph of the absolute value parent function, f(x) = |x|.
It is important to note that the absolute value parent function is not the only type of absolute value function. More complex absolute value expressions can include additional terms, like f(x) = |x – a| + b, where “a” and “b” are some constants. These modifications can result in shifts and translations of the basic V-curve.
By understanding the properties and graph of the absolute value parent function, you can better understand and graph more complicated absolute value functions.
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