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Active Prelude to Calculus

Activity 1.3.4.
Sketch at least two different possible graphs that satisfy the criteria for the function stated in each part. Make your graphs as significantly different as you can. If it is impossible for a graph to satisfy the criteria, explain why.
(a)
\(f\) is a function defined on \([-1,7]\) such that \(f(1) = 4\) and \(AV_{[1,3]} = -2\text{.}\)
(b)
\(g\) is a function defined on \([-1,7]\) such that \(g(4) = 3\text{,}\) \(AV_{[0,4]} = 0.5\text{,}\) and \(g\) is not always increasing on \((0,4)\text{.}\)
(c)
\(h\) is a function defined on \([-1,7]\) such that \(h(2) = 5\text{,}\) \(h(4) = 3\) and \(AV_{[2,4]} = -2\text{.}\)