Which function has the smallest minimum?

Question

anonymous · Answer

attachment

trantom · Answer

where are f(x) and h(x)?

anonymous · Answer

what do you mean? they're both there

trantom · Answer

oh oops I only saw the graph I though the equation table and graph were all g(x)

trantom · Answer

well g(x) is ruled out right away since it's minimum is 6 and h(x)'s is 5

anonymous · Answer

TRUE

trantom · Answer

so let me ask you this:
what is the amplitude of sin(x) (how far away does it get from the x axis?)

anonymous · Answer

you mean f(x)?

anonymous · Answer

wouldn't it be 4?

trantom · Answer

no we're just talking about plain old y=sin(x) right now

trantom · Answer

or well ok I guess you skipped that step so yea you're right xD

trantom · Answer

ok so in a vertex form quadratic equation, (which is what f(x) is except is has a sin function in it) the "c" (11) is how far it is raised from the x axis, and we know the amplitude is 4, which means it's minimum is 11-4=7

trantom · Answer

or sorry not a quadratic but anyway the point is that 11 is how far it is raised

anonymous · Answer

oh ok so the answer is h(x), right?

trantom · Answer

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anonymous · Answer

i see

trantom · Answer

yes, the answer is h(x)

anonymous · Answer

thank you so much! u did a great job explaining it!

trantom · Answer

your welcome! :)