表达式1: "y" equals left brace, negative 2 less than "x" less than 2 : abs left parenthesis, "x" , right parenthesis minus 1 , right bracey=−2<x<2:absx−1 1 表达式2: "y" equals left brace, negative 2 less than "x" less than 0 : negative 1 half "x" squared minus "...
Answer to: The graph of a piecewise function f(x) = |x| for x \lt 0 and f(x) = x^2 for x \gt 0 is steepest when {Blank}. By signing up, you'll get...
Example 2 Graph the piecewise function shown below. Using the graph, determine its domain and range. 2x , for x ≠ 01, for x = 0Solution For all intervals of x other than when it is equal to 0, f(x) = 2x (which is a linear function). To graph the linear function, we can us...
A Function Can be in PiecesWe can create functions that behave differently based on the input (x) value.A function made up of 3 piecesExample: Imagine a function when x is less than 2, it gives x2, when x is exactly 2 it gives 6 when x is more than 2 and less than or equal ...
A piecewise function is a function created using two or more functions on distinct domains. That is, a piecewise function is made from two or more functions that are defined on their own domains. Here is what a piecewise function will look like: P(x)={f(x)D1g(x)D2h(x)D3 In the ...
What is a Piecewise Function? A piecewise function is a function defined by a series of intervals for the independent variable. It shows a different function for a particular interval of real numbers. Take the example below: {eq}f(x)= \left\{\begin{matrix} x^2\,,for\, x<-1\\3x-1...
This article points out the methods to solve the derivative of piecewise function and discusses the derivative problem at point of demarcation of piecewise function in detail.───本文主要叙述分段函数的求导方法,并对分段函数在分界点处的求导作了细致的讨论。 Piecewise function is used to describe curv...
1-5. 2 Consider the piecewise defined function x2 +1 if x < 0 f(x) = cos(x) if 0 < x < 3 X-4 if x > 3 = 1. Find Limx-0-f(x) and Limx-50+f(x) 2. Is f continuous at x = 0 ? 3. Find Limx-3-f(x) and ...
Example 13: Graphing a Piecewise Function Sketch a graph of the function. f(x)=⎧⎨⎩x2 if x≤13 if 1<x≤2x if x>2f(x)={x2 if x≤13 if 1<x≤2x if x>2 Solution Each of the component functions is from our library of toolkit functions, so we know their shapes. We can...
Example 18Evaluating limits of a piecewise-defined function Let f(x)=(x-2)2 1x2as shown in Figure 1.22. Evaluate the following.1. lim_(x→1)f(x)5. lim_(x→0)f(x)x→1-x→0+2. lim_(x→1)f(x)6.f(0)x→1+3. lim_(x→1)f(x)7. lim_(x→2)f(x)x→2-x→14....