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Which is a valid prediction about the continuous function
f(x)?
f(x) < 0 over the interval (-00, 0).
f(x) > 0 over the interval (-1,00).
f(x) > 0 over the interval [-1, 1].
f(x) < 0 over the interval (0, 2).
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Which is a valid prediction about the continuous function fx fx lt 0 over the interval 00 0 fx gt 0 over the interval 100 fx gt 0 over the interval 1 1 fx lt 0 class=

Respuesta :

Answer:

Option C.

Step-by-step explanation:

Note: In option C interval should be (-1,1) instead of [-1,1].

From the given table it is clear that the value of f(x) is 0 at x=-1 and x=1.

The value of f(x) is negative over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]. So,

[tex]f(x)<0[/tex] over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]

The value of f(x) is positive over the interval [tex](-1,1)[/tex]. So,

[tex]f(x)>0[/tex] over the interval [tex](-1,1)[/tex]

Therefore, the correct option is C.

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