Finding Constants for Continuity of Composite Function

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Homework Help Overview

The problem involves finding constants a and b to ensure the continuity of a piecewise function defined over the entire real line. The function has different expressions depending on the value of x, and the continuity at the transition points is the focus of the discussion.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to establish equations based on the continuity conditions at the boundaries of the piecewise function. There is an exploration of how to set up and solve these equations to find the constants.

Discussion Status

Some participants have provided guidance on forming the necessary equations for continuity, while others express uncertainty about the solving process. There is an indication that multiple interpretations of the problem are being explored, but no consensus has been reached.

Contextual Notes

One participant notes the lack of an algebra book, which may affect their ability to follow through with the algebraic solutions discussed. There is also a mention of posting etiquette regarding new problems in the forum.

dylmans
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Homework Statement


Find the constants a and b such that the function is continuous on the entire real line.


Homework Equations


f(x)={2, x< or = -1
{ax + b, -1<x<3
{-2, x> or = 3


The Attempt at a Solution


I don't know where to start.

If anyone is willing to help me with my calculus make up work let me know. I don't get it at all.
 
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This isn't really calculus. You need to pick a and b so that a*(-1)+b=2 and a*(3)+b=-2. Do you see why?
 
haha sorry it is in my calculus book. you i think i do. but how would you get a and b then?
 
You would solve the two simultaneous equations -a+b=2 and 3a+b=(-2). I think that's in your algebra book.
 
a=-1 and b=1, i don't have an algebra book but i got it somehow. do i need a new thread for each new problem i have?
 
dylmans said:
a=-1 and b=1, i don't have an algebra book but i got it somehow. do i need a new thread for each new problem i have?

You don't have to. But you'll get better response time if you do. Posts with zero replies get much more attention.
 

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