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Explain the difference between the graphs of inverse variation functions When k > O and when k < 0.

User Jproton
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Answer:

Explanation:

Inverse variation functions have the form y = k / x, where k is a constant.

When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.

On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.

In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.

User Thumbmunkeys
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