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What type of curves does the equation y = k/x represent?
What type of curves does the equation y = k/x represent?
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Q1
What type of curves does the equation y = k/x represent?
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The equation y = k/x represents a family of hyperbolas where k is a constant.
Questions & Step-by-step Solutions
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Q: What type of curves does the equation y = k/x represent?
Solution:
The equation y = k/x represents a family of hyperbolas where k is a constant.
Steps: 5
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Step 1: Understand the equation y = k/x. Here, 'y' is the output, 'k' is a constant number, and 'x' is the input.
Step 2: Recognize that as 'x' changes, 'y' will also change based on the value of 'k'.
Step 3: Notice that when 'x' is positive, 'y' will also be positive, and when 'x' is negative, 'y' will be negative.
Step 4: Realize that the graph of this equation will not touch the x-axis or y-axis, creating two separate curves.
Step 5: Understand that these curves are called hyperbolas, which are a type of curve that opens away from each other.
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