Hello everyone. Im having trouble with a certain problem. It asks f(x)= 2x+3/x^2-4 (this is a fraction). I understand how to find the domain, but where im having trouble is finding the set of points where f is continuous. Do I have to graph the fraction to find where f is continuous? Is the fact that their will be a vertical asymptote make the problem discontinuous at a certain point? thank you.
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Finding set of points where f is continuous.
- Thread starter kidmo87
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Hello everyone. Im having trouble with a certain problem. It asks f(x)= 2x+3/x^2-4 (this is a fraction). I understand how to find the domain, but where im having trouble is finding the set of points where f is continuous. Do I have to graph the fraction to find where f is continuous? Is the fact that their will be a vertical asymptote make the problem discontinuous at a certain point? thank you.
You are correct; the function will be discontinuous at the vertical asymptotes.
One more about continuous function.
Hello. So that I understand if domain plays a factor in continuities. If the square root of 3x+4 (the whole problem is in the square root). Since the domain is -4/3 (fraction). The discontinuity would also be-4/3? or not because the graph would be going towards the first quadrant, and the line on the graph would never approach the vertical asymptote? thanks.
Hello. So that I understand if domain plays a factor in continuities. If the square root of 3x+4 (the whole problem is in the square root). Since the domain is -4/3 (fraction). The discontinuity would also be-4/3? or not because the graph would be going towards the first quadrant, and the line on the graph would never approach the vertical asymptote? thanks.
Hello. So that I understand if domain plays a factor in continuities. If the square root of 3x+4 (the whole problem is in the square root). Since the domain is -4/3 (fraction). The discontinuity would also be-4/3? or not because the graph would be going towards the first quadrant, and the line on the graph would never approach the vertical asymptote? thanks.
Be careful what you are saying (and thinking). First of all, the domain is not "-4/3" -- nor is it all real numbers except "-4/3". Do not treat square roots the same way as denominators.
Denominators may not equal zero, so we set denominators equal to zero and solve in order to determine what our domain does not include.
Square roots have different constraints; one cannot take the square root of a negative number. Therefore, we set up the expression inside the square root as an inequality. For f(x) = (3x + 4)^(1/2), 3x + 4 must be greater than or equal to zero. This will determine the domain: [-4/3, infinity).
ok. so instead of having the square root of 3x+4, i should make it (3x+4)^(1/2)? Then solve to get the Domain? So how could i use this to find where f is continuous. Sorry, please dont think im trying to get you to do my work, i just really need to understand how to come up with where it is continuous from. Thank you.
ok. so instead of having the square root of 3x+4, i should make it (3x+4)^(1/2)? Then solve to get the Domain? So how could i use this to find where f is continuous. Sorry, please dont think im trying to get you to do my work, i just really need to understand how to come up with where it is continuous from. Thank you.
The square root of (3x+4) is the same as (3x+4)^(1/2) -- just two different ways of writing the same thing. A square root is just something to the (1/2) power.
If a function has a domain of [-4/3, infinity), then it is continuous over that same interval.
In another example, if the domain is (-infinity, -5)U(-5, 7)U(7, infinity), then the function is discontinuous at -5 and 7 but continuous everywhere else.
HallsofIvy
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A function cannot be continuous at a point which is not in domain because part of the definition of "f is continuous at x= a", is that f(a) exist- i.e. that a be in the domain.
Further, all of the "elementary functions", polynomials, rational functions, exponentials, trig functions, etc. are continuous at every point in their domain.
Further, all of the "elementary functions", polynomials, rational functions, exponentials, trig functions, etc. are continuous at every point in their domain.