Mark M. answered • 10/21/20
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Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.
Answer: b, due to the Intermediate Value Theorem.
Mark M.
tutor
The Intermediate Value Theorem states that: if f(x) is continuous on the interval [a,b], and if d is a number between f(a) and f(b), then there is a number c in the interval (a,b) such that f(c) = d. So, in your problem, let a = 1, b = 5, f(a) = -2, f(b) = 7, and d = 0, and assume that f(x) is continuous on [1,5]. In other words, (1, -2) is a point on the graph of y = f(x) that lies below the x-axis and (5, 7 ) is on the graph of y = f(x) that lies above the x-axis. So, if f(x) is continuous on [1,5], then the graph must cross the x-axis at least once between x = 1 and x = 5.
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10/22/20
Mary C.
can you explain more details10/21/20