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I need help. I’m lost with pre calculus and failing miserably.

I need help. I’m lost with pre calculus and failing miserably.-example-1
User Visal Rajapakse
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1 Answer

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24 votes

Ajump discontinuity means that for a given "x" value the function gives a "y" values and just next to it it jumps to a completly different "y" value. In the graph, we can spot them when there is a discontinuity in it.

This is simply a part that you would have to jump to a value.

The parts where this happens in this case are the marked below:

Notice that in the first, the function jumps from y = 0 to y ≈ -5 at x ≈ 6.

And lastly, it jumps from y ≈ -3 yo y = -1 at x = 3.

In these parts, the lateral limits exist, but aren't the same, so the function jumps from one place to the other.

Notice, however, that de function have empty dots at x = -2 and x = 2, but without a replacement for it, that is, the function is simply undefined in thouse places. This is not a jump discontinuity, so they don't count (they are another type of discontinuity).

Also, at x = 0, the function has a point that is out of the tendency, that is, the lateral limits exist and are the same, but the actual function value is different. This also doesn't count.

Since the two discontinuities are in the interval -9 < x < 9, all of them must be in the answer.

So, the answer is, the jump discontinuities are: at:


\begin{gathered} x=-6 \\ x=3 \end{gathered}

I need help. I’m lost with pre calculus and failing miserably.-example-1
User Tawfik
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2.8k points