1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Piece-wise defined functions

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations
    The transformations of the function of f(t) are:
    h(t)= f(t)-2 and k(t)= 3-2f(t-2)


    3. The attempt at a solution

    I understand that a piecewise function is defined with different
    formulas. In this case, all formulas are linear or straight lines in
    a form of y=mx+c.Here I'm not sure: The first formula; f(t)= t+4,
    provided -4<=t<0 is a line with a of slope of 1 and an x-intercept
    of t=4; but we are only supposed to sketch that part of a line that
    lies to the left or at t=4.Therefore,f(4)=4+4=8 :fixed endpoint of
    the ray is (4,8)

    Thank
     
  2. jcsd
  3. Mar 18, 2010 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    What you are saying is correct so I don't see what your difficulty is.

    The graph of y= t+ 4 is a straight line. When t= -4, y= 0 and when t= 0, y= 4 so it is straight line segment with endpoints (-4, 0) and (0, 4). It includes (-4, 0) but not (0, 4).

    The graph of (-3/2)t+ 10 is a straight line segment with endpoints (0, 10) and (2, 7). It includes (0, 10) but not (2, 7).

    The graph of (1/2)t is a straight line segment with endpoints (1, 1) and (4, 2). It includes both (1, 1) and (4, 2).
     
  4. Mar 23, 2010 #3
    Hi HallsofIvy, I understand now, but the last graph isn't supposed to be (2,1) because when t=2 ,y=1...I think you made a little error.

    I tried to plot the f(t) using Derive6, here is my sketch below: I'm not sure with the transformations, h(t) and k(t). Please help. Thanks
     

    Attached Files:

    Last edited: Mar 23, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Piece-wise defined functions
Loading...