How do you graph # f(x)= x/(x+3)#?
graph{1-3/(x+3) [-10, 10, -15, 15]}
graph{1/x [-10, 10, -15, 15]}
graph{1/(x+3) [-10, 10, -15, 15]}
graph{3/(x+3) [-10, 10, -15, 15]}
graph{-3/(x+3) [-10, 10, -15, 15]}
graph{1-3/(x+3) [-10, 10, -15, 15]}
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To graph the function f(x) = x/(x+3), follow these steps:
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Determine the domain of the function, which is all real numbers except for x = -3 (since division by zero is undefined).
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Find the y-intercept by substituting x = 0 into the equation: f(0) = 0/(0+3) = 0/3 = 0. So, the y-intercept is (0, 0).
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Determine the x-intercept by setting f(x) = 0 and solving for x: x/(x+3) = 0. This occurs when x = 0, so the x-intercept is (0, 0).
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Analyze the behavior of the function as x approaches positive and negative infinity. As x approaches infinity, f(x) approaches 1. As x approaches negative infinity, f(x) approaches -1.
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Plot additional points by choosing various x-values and calculating the corresponding y-values using the equation.
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Draw a smooth curve passing through the plotted points, considering the behavior of the function and the asymptotes.
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Finally, label the x and y axes, and any other relevant points or features on the graph.
Note: The graph will have a vertical asymptote at x = -3, as the function approaches infinity as x approaches -3 from the left, and approaches negative infinity as x approaches -3 from the right.
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When evaluating a one-sided 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 one-sided 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 one-sided 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 one-sided 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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- What are the asymptotes of #y=2/(x+1)-4# and how do you graph the function?
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