All functions have certain properties, or distinct features, which can be very useful when trying to analyze them. The following common properties of functions describe how a graph is shaped, what happens as x-values increase, and whether the functions can be further analyzed with calculus: Domai...
The following examples are based on this graph of a piecewise function which has a jump at x = 1: Example question 1: What is the limit of f(x) as x approaches 2? Solution:“f(x)” is the function value at 2 (a.k.a. the y-value). We want to know what’s happening to the...
Anabsolute value functionhas a unique “V” shape when plotted on a graph. This is due to the fact that the absolute value of a negative number makes that number positive. The absolute value parent function. The absolute value parent function is written as: f(x) = │x│ where: ...
Graph of f(x) = (2/π) sin-1[sin (π x)] created on Desmos.com Creating a Triangle Wave with Piecewise Functions Onerelatively simple way to create a graphof the triangle wave function is to construct a series ofpiecewise functions. In other words, each individual “tooth” can be bu...