To compare the functions \( f(x) = (x + 2)^2 \) and \( g(x) = 2x + 4 \), we first observe their shapes. The function \( f(x) \) is a quadratic function, which means it has a parabolic shape that opens upwards, with its vertex at the point (-2,0). In contrast, \( g(x) \) is a linear function, represented by a straight line with a slope of 2 and a y-intercept at 4.
In terms of similarities, both functions are continuous and defined for all real numbers. However, they differ significantly in behavior: \( f(x) \) has a minimum point and exhibits symmetry about its vertex, while \( g(x) \) has a constant rate of change and does not have any turning points. Additionally, \( f(x) \) demonstrates quadratic growth, whereas \( g(x) \) demonstrates linear growth.
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