How do you graph #y= x/(x4)#?
Have a look:
Let us study our function in steps:
1) Domain (
we need the denominator different from zero:
2) Intercepts:
set:
set:
3) Limits:
4) Derivatives:
FIRST:
set:
SECOND:
set
you get:
graphically:
graph{x/(x4) [10, 10, 5, 5]}
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To graph the equation y = x/(x4), you can follow these steps:

Determine any restrictions on the domain. In this case, the denominator (x4) cannot be equal to zero, so x ≠ 4.

Find the yintercept by substituting x = 0 into the equation: y = 0/(04) = 0/(4) = 0.

Find the xintercept by setting y = 0 and solving for x: 0 = x/(x4). Since the numerator is zero, x = 0. However, this value is not valid since it would make the denominator zero. Therefore, there are no xintercepts.

Determine the behavior of the graph as x approaches positive and negative infinity. As x approaches positive infinity, y approaches 1. As x approaches negative infinity, y approaches 1.

Plot additional points to sketch the graph. Choose various xvalues (excluding x = 4) and calculate the corresponding yvalues. For example, when x = 2, y = 2/(24) = 2/(6) = 1/3. Repeat this process for other xvalues.

Connect the plotted points smoothly to form the graph.
The graph of y = x/(x4) will have a vertical asymptote at x = 4 and will approach positive infinity as x approaches positive infinity, and negative infinity as x approaches negative infinity.
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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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