A2-column table with 8 rows. the first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20. which could be the entire interval over which the function, f(x), is positive? (–∞, 1) (–2, 1) (–∞, 0) (1, 4)

Step-by-step explanation:

So I'm going to  make the table here.

x     f(x)

-3     -2

-2     0

-1     2

0     2

1     0

2     -8

3     -10

4     -20

Without looking at the answers we are going to deduce what intervals could make f(x) positive.  Well, where  is it shown as positive for the numbers given?  well f(-1) and f(0) are positive, both at 2.  then both f(-2) and f(1) are 0, then everything below -2 and above 1 make f(x) negative, so it looks like everything up until -2 is negative, but increasing then at -2 it turns to 0 and keeps increasing  at least until some time after f(-1).  It might even just stay at 2 until it gets to f(0), and then after that it decreases.  Hopefully that makes sense.

Given the description, and if you on't understand I can try to explain more carefully, where does it look like it's positive?  Well, it goes from negative to 0 at -2, then after that it's positive until 1, where it turns to 0 again, before decreasing.    so everything between -2 and 1 look to make f(x) positive.  Since f(-2) and f(1) don't themselves though it means they are not included, so you use parenthesis.

so the answer is (-2,1)  Again, let me know if you need more of an explanation.