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What type of curves does the equation y = mx^3 + c represent?
What type of curves does the equation y = mx^3 + c represent?
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Q1
What type of curves does the equation y = mx^3 + c represent?
Linear functions
Cubic functions
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Exponential functions
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The equation y = mx^3 + c represents a family of cubic functions where m is the coefficient of x^3.
Questions & Step-by-step Solutions
1 item
Q
Q: What type of curves does the equation y = mx^3 + c represent?
Solution:
The equation y = mx^3 + c represents a family of cubic functions where m is the coefficient of x^3.
Steps: 6
Show Steps
Step 1: Identify the equation given, which is y = mx^3 + c.
Step 2: Recognize that 'm' is a number that affects the steepness and direction of the curve.
Step 3: Understand that 'c' is a constant that shifts the curve up or down on the graph.
Step 4: Realize that since the highest power of x is 3, this is a cubic function.
Step 5: Note that cubic functions can have different shapes depending on the value of 'm'.
Step 6: Conclude that the equation represents a family of curves that can look different based on 'm' and 'c'.
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