How do you graph and find the discontinuities of #F(x) = (2x^2 + 1)/(2x^3 + 4x^2)#?
Solve for the asymptotic discontinuities
We can separate this into two equations:
As for graphing, you can do that by creating a table of values.
It should end up like this: graph{(2x^2+1)/(2x^3+4x^2) [10, 10, 5, 5]}
You will notice that the graph looks like it's approaching x=0 and x=2, but it will never actually touch it.
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To graph and find the discontinuities of the function F(x) = (2x^2 + 1)/(2x^3 + 4x^2), follow these steps:

Determine the domain of the function by identifying any values of x that would make the denominator equal to zero. In this case, set the denominator equal to zero and solve for x: 2x^3 + 4x^2 = 0 Factor out common terms: 2x^2(x + 2) = 0 Set each factor equal to zero and solve for x: 2x^2 = 0 or x + 2 = 0 x = 0 or x = 2

The domain of the function is all real numbers except for x = 0 and x = 2.

To graph the function, plot points by substituting various xvalues into the equation and calculating the corresponding yvalues. You can choose values such as 3, 2, 1, 0, 1, 2, and 3 to get a sense of the shape of the graph.

Determine the behavior of the function as x approaches the values where the function is not defined (discontinuities). In this case, as x approaches 0 or 2, the function approaches positive or negative infinity, respectively.

Plot the points obtained from step 3 on a graph and connect them smoothly to form the graph of the function, taking into account the behavior near the discontinuities.
Note: It is recommended to use graphing software or a graphing calculator to visualize the graph accurately.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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