Then, simplify the equation given by distributing and combining like terms.ĥ Example: Write y = 2 Ix – 4I – 10 as a piecewise function. This is the Absolute Value Function: f(x) x It is also sometimes written: abs(x). The vertex form of an absolute value graph function is y a x h + k The. Piecewise functions are functions with more than one piece. For I x - h I < 0, substitute –(x - h) in place of I x - h I. An absolute value function is a piecewise function whose graph has a V shape. We can graph absolute value functions by translating them into piecewise functions. For I x - h I ≥ 0, simplify the equation given by distributing and combining like terms.
To identify the number in the domain, set x – h = 0 and solve for x.
We usually write an absolute value function as f (x)= x, but since absolute value is a measure of distance and distance is always positive, it also can be written as follows: -x, if x < 0 x, if x ≥ 0 f (x) = Piecewise Functions The mean value theorem states that under the specified hypotheses, there is a point in the interval of interest such that the slope of the tangent line at that point is equal to the slope of the secant line connecting the two endpoints of the graph of the function This action combines the two piecewise expressions The limit.