The function \( f(x) = (x + 2)^2 \) represents a quadratic function, which has a parabolic shape that opens upwards. Its vertex is at the point (-2, 0), indicating the lowest point of the graph, and it is symmetric about the line \( x = -2 \). In contrast, \( g(x) = 2x + 4 \) is a linear function, resulting in a straight line with a slope of 2 and a y-intercept at 4.
The key similarity between the two functions is that they both represent polynomial functions and can be evaluated for any real number \( x \). However, they differ in their shapes and characteristics: \( f(x) \) is nonlinear and has a vertex, while \( g(x) \) maintains a constant rate of change and does not have any curves or points of inflection. Additionally, \( f(x) \) includes the squared term, leading to its parabolic form, while \( g(x) \) is simply a linear expression.
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