I have a test tomorrow and this is a subject we only briefly touched on. I can find points of discontinuity graphically very easily, but I have no idea how to find them algebraically using just the equation.(adsbygoogle = window.adsbygoogle || []).push({});

I know that when the denominator = 0 and in most piecewise functions there is discontinuity. I suppose i'll put up a couple of examples.

[tex]\frac {x} {2x^2+x}[/tex]

I cancelled the x on this one which made the graph eqn look like a 1/x graph, which I know is not continuous at x=0, but it is also not continuous at x=-1/2 and I don't know why.

[tex]\frac {3} {x} + \frac{x-1} {x^2-1}[/tex]

I assume that I can use one of the theorems which states that if both f(x) and g(x) are continuous then f(x)+g(x) is continuous? I'm stumped on how to find the discontinuities.

[tex]\frac {x^2+6x+9} {|x|+3}[/tex]

I assume the answer is continuous everywhere here, since you cannot have a 0 on the denominator.

Also consequently, what is the standard 'working' that you should show for these problems in your answer?

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# Homework Help: Finding Discontinuity Algebraically

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