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

Answer 1

Let me the multiple choices?

Answer 2

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

Answer 3

If touches f(x)=0 once that mean it touches y=0 once

What do you think it is now?

Answer 4

0?

Answer 5

x value is the horizontal coordinate.
They are looking which x value can be f(x)=0

Answer 6

If they say it can only touch f(x)=0 or (y=0) once, that means it will always increase since the graph from f(-7) to f(-2) is increasing.

Answer 7

well I figured it might be -3 because -2=10 and -7=-5 so it would have to be between them right?

Answer 8

and it will always decrease from f(-7) to f(-10) and so on.

Answer 9

Yes, you are correct, it is -3.

Answer 10

thank you

Answer 11

No problem!