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An absolute value function is an important function in algebra that consists of the variable in the absolute value bars. The general form of the absolute value function is f (x) = a |x - h| + k, where (h, k) is the vertex of the function.
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To simplify an algebraic expression, we just combine the...
- Inverse of a Function
Finding the Rule. To find the function rule for an absolute value function, we need 3 points on the graph. If however one of those points is the vertex, we only need 2 points: the vertex and one other point. Here are 2 examples illustrating the procedure for finding the function rule. Example.
In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.
An absolute value function is represented by the equation: \[ f(x) = a|x - h| + k \] Here, \(a\) determines the slope; \(h\) shifts the graph left or right, and \(k\) shifts the graph up or down. The absolute value of a number \(x\) is its distance from zero on the number line.
21 wrz 2023 · Absolute value equations can have up to two solutions. To solve an absolute value inequality involving “less than,” such as \(|X| ≤ p\), replace it with the compound inequality \(−p ≤ X ≤ p\) and then solve as usual.
The absolute value function can be defined as a piecewise function. f(x) = |x| = {x if x ≥ 0 − x if x <0. Example 1. Using Absolute Value to Determine Resistance. Electrical parts, such as resistors and capacitors, come with specified values of their operating parameters: resistance, capacitance, etc.
Learning Objectives. Graph an absolute value function. Solve an absolute value equation. Until the 1920s, the so-called spiral nebulae were believed to be clouds of dust and gas in our own galaxy, some tens of thousands of light years away.
