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How does one express the values of the function f(x) as x approaches 3?

User Mone
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Final answer:

One expresses the values of the function f(x) as x approaches 3 by analyzing its behavior near that point. For a function with a positive value and a slope that is positive but decreasing as x increases, the quadratic function y = x² matches the criteria as it increases at a decreasing rate near x = 3.

Step-by-step explanation:

To express the values of the function f(x) as x approaches 3, you consider the behavior of the function near that point. If a function f(x) has a positive value and a positive slope that is decreasing as x increases near x = 3, we are looking for a function that is increasing but at a decreasing rate at x = 3. Given the options provided:

  • y = 13x is a linear function with a constant slope, which is not decreasing.
  • y = x² is a parabolic function that has a positive slope that decreases as x moves from 0 to its vertex and then increases again, which matches the description for x < 3.

Therefore, the option that could correspond to f(x) as given in the scenario is b. y = x².

User Nayagam
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