If f(x) is a continuous function defined for all real numbers, f(–2) = 10, f(7) = –5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value.

a. -3
b. -8
c. 0
d. 2

Question

If f(x) is a continuous function defined for all real numbers, f(–2) = 10, f(7) = –5, and f(x) = 0 for one and only one value of x, then which of the following could be that x value.

a. -3
b. -8
c. 0
d. 2

aryana_maria2323 · Answer

@agent0smith

bobo-i-bo · Answer

O.o Have you done Analysis I/II yet? Do you know the Intermediate Value Theorem?

aryana_maria2323 · Answer

No I do not know what the Intermediate Value Theorem is.

agent0smith · Answer

I'd plot the given points on a graph and that might help you.

aryana_maria2323 · Answer

I tried that and all I got was the points. None of the answers fit.

agent0smith · Answer

I see two that would fit and make sense.

welshfella · Answer

0 and 2?

agent0smith · Answer

The points (-2, 10) and (7, -5) give you a limited area where you could have an x-intercept

welshfella · Answer

i'm afraid i've forgotten much of this stuff...

agent0smith · Answer

|dw:1459811226324:dw|

A continuous function CANNOT get from A to B, without passing through the x-axis...

welshfella · Answer

right

aryana_maria2323 · Answer

Okay so if both 0 and 2 work. How do I determine which is the correct answer?

bobo-i-bo · Answer

Hmmm, basically, a continuous function is a function which you can graph without lifting the pen off the page. For example:|dw:1459811262262:dw|