To describe a curved line with a negative slope that begins at (0, 0) and extends toward negative infinity, we can consider a class of functions that generally exhibit this behavior. One common type of function that fits this description is a decreasing function, such as a negative exponential function or a negative power function.
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Negative Exponential Function: An example could be: \[ f(x) = -e^{-x} \] This function starts at (0, 0) and decreases toward negative infinity as \( x \) increases.
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Negative Power Function: Another example could be: \[ f(x) = -x^2 \] This function also starts at (0, 0) and decreases towards negative infinity as \( x \) moves away from zero.
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Logarithmic Functions: A logarithmic function with a negative constant might also work, such as: \[ f(x) = -\ln(x+1) \] This also curves down, starting at (0, 0) and continuing toward negative infinity as \( x \) increases.
Each of these equations describes a function that starts at (0,0) and has a negative slope, trending downwards toward negative infinity. If you are looking for a specific function family or type of function to match a certain graph, it's helpful to have more detail about the behavior or shape you expect.
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