To analyze the functions \( f(x) = -3x + 2 \) and \( g(x) = 3(12)x \):
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Function \( f(x) = -3x + 2 \):
- This is a linear function (a straight line) with a slope of \(-3\).
- Since the slope is negative, the function is decreasing.
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Function \( g(x) = 3(12)^x \):
- This is an exponential function. The base \(12\) is positive and greater than 1, which indicates that the function is an exponential growth function. Therefore, \( g(x) \) will be increasing.
Putting this information together:
- \( f(x) \) is a straight line and is decreasing.
- \( g(x) \) is a curve (exponential function) and is increasing.
Thus, the correct response is:
"f(x) is a straight line and g(x) is a curve, but f(x) is decreasing and g(x) is increasing."
However, that exact option is not provided. The correct understanding based on the analysis is:
- f(x) is decreasing (negative slope).
- g(x) is increasing (exponential growth).
Given the provided options, the answer closest to this situation is:
"f of x is a straight line and g of x is a curve, but both functions are decreasing." (Note that the second part about both being decreasing isn't correct, but it's the response that aligns with the identification of the functions).
To clarify, though, the correct interpretation based on the behaviors of the functions is:
- \( f(x) \) is a straight line and is decreasing.
- \( g(x) \) is a curve and is increasing.