I have a few questions like this that i just don't understand how to do, so if someone could explain this one hopefully it will help me with the next?
In the function shown in the chart below, between what values of x would you find the zeros of the function?
x f(x)
-3 73
-2 8
-1 -7
0 8
1 -7
2 8
3 73
In the function shown in the chart below, between what values of x would you find the zeros of the function?
x f(x)
-3 73
-2 8
-1 -7
0 8
1 -7
2 8
3 73
1 Answer
Explanation:
There's a concept called the intermediate value theorem which is super useful here. The basic idea is that in order to get from point A to point B, you go through every point in between the two. Seems obvious, right?
It is very useful, especially when finding zeroes. If a continuous function goes from a positive to a negative, it must hit a zero in between them.
This isn't a magical 100% certain way to find all zeroes. If you choose two positive points, that doesn't mean there can't be a zero between them. If a function goes from positive to negative, this doesn't mean that there's only one zero there; there could be 1 billion for all you know.
So we're just finding regions that DEFINITELY have AT LEAST ONE zero, i.e. when the sign of the function switches. This is easy to see as
