Problem

Compare \(f(x)~=~2x~+~7\) and \(g(x)~=~-x~+~9\) using their initial values and rates. Calculate the crossover point and state the function comparison on either side.

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initials = f(0)=7 and g(0)=9, so g starts 2 higher; rates = f slope 2 increasing and g slope -1 decreasing; crossover = none; comparison = g>f for all x because it starts higher

initials = f(0)=7 and g(0)=9, so g starts 2 higher; rates = f slope 2 increasing and g slope -1 decreasing; crossover = x=2/3, point (2/3,25/3); comparison = g>f for x<2/3, equal at 2/3, f>g for x>2/3

initials = f(0)=7 and g(0)=9, so f starts higher; rates = f slope 2 decreasing and g slope -1 increasing; crossover = x=2/3, point (2/3,25/3); comparison = f>g for x<2/3, equal at 2/3, g>f for x>2/3

initials = f(0)=7 and g(0)=9, so g starts 2 higher; rates = f slope 2 increasing and g slope -1 decreasing; crossover = x=2, point (2,11); comparison = g>f for x<2, equal at 2, f>g for x>2

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Compare \(f(x)~=~2x~+~7\) and \(g(x)~=~-x~+~9\) using their initial values and rates. Calculate the crossover point and state the function comparison on either side.

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