Mathematics

Examine the following graph of the linear function f(x)=2x+1 and the quadratic function g(x)=−116(x+3)2+6.
Graph of g of x is a downward opening parabola that passes through points (negative 4, 5), (negative 3, 6), & (1, 5). f of x is a line that passes through points (negative 4, negative 7), (0, 1), & (3, 7).

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Which statements about the functions are true?

Over the interval 4≤x≤6, the average rate of change of g(x) is faster than the average rate of change of f(x).
Over the interval −8≤x≤−7, the average rate of change of g(x) is slower than the average rate of change of f(x).
Over the interval 0≤x≤3, the average rate of change of g(x) is the same as the average rate of change of f(x).
Over the interval \(-8 \le x \le -3\textsf{,}\) the average rate of change of \(g(x)\) is slower than the average rate of change of \(f(x)\textsf{.}\)
Over the interval \(4 \le x \le 6\textsf{,}\) the average rate of change of \(g(x)\) is slower than the average rate of change of \(f(x)\textsf{.}\)
Over the interval \(-3 \le x \le 2\textsf{,}\) the average rate of change of \(g(x)\) is faster than the average rate of change of \(f(x)\textsf{.}\)

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