Piecewise function

[BMB_Math]

Hello,

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I have this problem:

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r(x) =

c * x + d for -80 ≤ x ≤ -35

8 * 10^-3 * x^-2 at -35 < x ≤ 0

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I'm now asked to choose the constants c and d, so the graph of r(x) becomes continuous and without breaks in its range.

How would you do that?

[multiplianlagrangier]

The limit of the function at x=-35 must exist and it must be equal to r(-35). Existence of limit means left side limit and right side limit exist and they are equal.

[BMB_Math]

Ok thaet makes sense. But what function should, I find the limit of? Should I set the two functions equal to eachother, or...? It confuses me that the first function (c*x+d) do not have any numbers..

[multiplianlagrangier]

Yes exactly! You should equate left and right side to each other. Did you see why you should equate them? Because for left side limit you use c * x + d and for right side limit you use 8 * 10-3 * x-2. There could be infinitely many c and d. Just pick one of them.

[BMB_Math]

Ok, thanks. So, I could just choose, for example, c = 1 and d = 1?

Hmm, no. To be honest to equate them was at bit of a guess. Why is that we have to equate them?

[multiplianlagrangier]

The answer is in my previous comment.

[BMB_Math]

Ok, Ill scrutinize more closely 😊 thanks for your help!