What is Piece-wise: Definition and 22 Discussions

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  1. C

    Showing piece-wise function continuous

    For this, , The solution is, However, should they not write ##f(x) = \cos x## on ##[\frac{pi}{4}, \infty)## Many thanks!
  2. T

    MHB Continuous, discontinuous and piece-wise function

    help me please to determine what are the equations i need tofinish my activity. Thankyou
  3. karush

    MHB 1.8.4 AP Calculus Exam Integral of piece-wise function

    image due to macros in Overleaf ok I think (a) could just be done by observation by just adding up obvious areas but (b) and (c) are a litte ? sorry had to post this before the lab closes
  4. J

    MHB Piece-Wise Linear Function

    This is an exercise given in my real analysis course. We have definitions for continuity, uniform continuity, l.s.c and u.s.c., but I don't see how to apply them. I guess I want to construct $φ$ piece by piece of the interval to eventually cover all of [a,b]? Exercise: A continuous function...
  5. S

    MHB Anatomy of piece-wise functions

    Hi! I'm looking at some piece-wise function right now and I can't help but wonder what all these parts are called. I'm learning to use and write this type of functions now and I think I have a pretty good understanding of how they work. I even took the extra step of learning some "set builder...
  6. 1

    Differentiability of piece-wise functions

    Hello, Me and my friend were talking about differentiability of some piece-wise functions, but we thought of a problem that we could were not able to come to an agreement on. If the function is: y=sin(x) for x≠0 and y=x^2 for x=0, Is this function differentiable? The graph looks like a normal...
  7. K

    Mathematica FindMaximum function in Mathematica

    I recently plotted a piecewise function: Plot[Piecewise[{{1 - Exp[-.002*t], 0 <= t < 120}, {-Exp[-.002*t] + Exp[-.002*(t - 120)], 120 <= t}}], {t, 0, 5000}, PlotRange -> {0, 0.25}] I then defined the function which I am calling q[t_] as follows: q[t_] := Piecewise[{{1 -...
  8. K

    Mathematica Troubleshooting Mathematica Plotting Problem

    Homework Statement I've entered the following piecewise equation into Mathematica: Plot[Piecewise[{{sin (t), 0 <= t < \[Pi]}, {5 + 5 cos (t) + sin (t), \[Pi] <= t < 4*\[Pi]}, {10 cos (t) + sin (t), 4*\[Pi] <= t}}], {t, 0, 20*\[Pi]}] But I am getting a blank graph in return. I've proofread my...
  9. P

    Proving a piece-wise defined function is bijective.

    Homework Statement ##f:\mathbb{Z} \to \mathbb{N}## ## f(x) = \begin{cases} 2x+2 & \text{if } x \geq 0 \\ -2x-1 & \text{if } x < 0 \end{cases} ## Prove that f is a bijection from ##\mathbb{Z}## to ##\mathbb{N}## Homework EquationsThe Attempt at a Solution Proving that it is an injection if quite...
  10. R

    How to Integrate g(x)=∫ƒ(t) dt from -5 to x | Homework Help

    Homework Statement http://s23.postimg.org/wsj9e91wb/IMG_1334.jpg[/B] photo of the problem g(x)=∫ƒ(t) dt from -5 to x ƒ(t) = (0 if x < -5 5 if -5≤x<-1 -3 if -1≤≤x<3 0 if x≥3) (a) g(-8) = 0 (b) g(-4) = 5 (c) g(0) = ? (d) g(4) = ? Homework Equations ∫ƒ(x) from...
  11. B

    Finding A Constant To A Piece-Wise Function

    The function is g(x) = (x^2 - a^2)/(x - a) if x doesn't equal a; and the second part is g(x) = 8 when x = a. The question asks for me to find a specific value for a so that the function might be continuous on the entire real line. I know that each part of the piece-wise function needs to...
  12. N

    Proving piece-wise function is one-to-one?

    f: Z -> Z defined by f(x) = x/2 if x is even, (x-1)/2 if x is odd. Proof: If x is even: x1 = 2k1 x2 = 2k2 Suppose f(x1) = f(x2), then 2k1/2 = 2k2/2 k1 = k2 So if x is even, the function is one to one? Is this an okay proof for the first half of if x is even, then I just do the...
  13. U

    Proving Differentiability of a Piece-wise Function

    1. Suppose f(x)=0 if x is irrational, and f(x)=x if x is rational. Is f differentiable at x=0? 2. the derivative= lim[h->0] [f(a+h)-f(a)]/h 3. I don't really know how to start, but I do know that between any two real numbers, there exists a rational and irrational number. So I'm...
  14. J

    Piece-Wise Function Continuity

    Homework Statement Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. f(x)= {x^3 if x < or = -2 {2 if x > -2 Homework Equations The conditions are that a function is said to be...
  15. T

    Simplifying Piecewise Functions: fg(x) and gf(x) Calculations

    Homework Statement Function f and g are defined as follows : f(R)=R , f(x)=x^2 , g(R)=R , g(x)=x+1,x>=0 , -x , x<0 (its a piecewise function) . Find fg(x) and gf(x) . Homework Equations The Attempt at a Solution fg(x)= (x+1)^2 , x>=0 x^2 , x<0 gf(x)= x^2+1 , x>=0...
  16. M

    Interesting piece-wise problem

    I hate a piece-wise function f(x)= [ 1 if 0 </eq x </1 [ 0 if 1 < x < 2 [ -2x+4 if x >/eq 2 If I let F(x)= integral (from 0->x) f(t) dt, how can i find a formula for F(x) without using integrals? I think it may have something to do with the 2nd definition of the...
  17. T

    How Do You Sketch and Transform a Piecewise-Defined Function?

    Homework Statement Please help me sketch the graph of the given piecewiswe-defined function and its transformations: The function f(t)={t+4 ;-4<=t<0 ={-3/2(t)+10 ; 0<=t<2 ={1/2(t) ; 2<=t<=4 Homework Equations The transformations of the...
  18. D

    Understanding the Role of Series Resistors in Piece-Wise Linear Diode Models

    I am NOT trying to solve this as a homework problem, I'm just trying to dig out basic concepts that I'm missing when using this battery+resistance diode model.I'm having trouble seeing why, when solving for current, KCL equation does NOT work out as: 1) I= (0-Va)/rd 2) I=(Va-(-5))/R...
  19. V

    Continuity on a piece-wise function

    [SOLVED] Continuity on a piece-wise function Problem: Suppose: f(x)=\left\{\begin{array}{cc}x^2, & x\in\mathbb{Q} \\ -x^2, & x\in\mathbb{R}\setminus\mathbb{Q}\end{array}\right At what points is f continuous? Relevant Questions: This is in a classical analysis course, not a...
  20. J

    Derivative of Piece-Wise Function

    I am doing my calculus homework and two problems are holding me up. The first says: Using one-sided derivatives, show that the function f(x) = x^3, x_<_1 3x, x>1 does not have a derivative at x=1 Now it is painfully obvious that the function is not continuous at x=1. however, i...
  21. S

    Solving Piece-wise Functions: y=|x|+x Graph Explained

    I'm doing a review of fuctions, and a nagging question popped up in my mind after completing this problem. After graphing y = |x| + x, express this equation as a piece-wise function with no absolute values. I did graph it; it was simple (following is a sketch without values)...
  22. P

    Piece-wise continuous functions on the close interval

    Let D[a,b] be the set of piece-wise continuous functions on the close interval [a,b]. Show that D[a,b] is a subspace of the vector space P[a,b] of all functions defined on the interval [a,b]. Can someone get me started? Do I just need to show that they are closed under addition and...