A 2-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

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3 years ago

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A 2-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)

Mathematics

2 answers:

IceJOKER [234] · Answer 1 · 2022-02-05T16:00:15+03:00

Answer:

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.