Question

X-3-2-101234ark this and returnf(x)-20220-8-10-20Which could be the entire interval over which thefunction, f(x), is positive?O (-∞, 1)O (-2, 1)O (-∞, 0)(1,4)Save and Exit

Answer 1

Solution

- The function is positive where the values of f(x) are positive.

- But the interval which defines the portion for which the function is positive, are the x-values.

- Thus, we should just look at the parts of the table where f(x) is greater than 0 and write down the x-values corresponding to these f(x) values.

- Thus, we have that the interval over which the function is positive is:

$\begin{gathered} x\to f(x) \\ -2\to0 \\ -1\to2 \\ 0\to2 \\ 1\to0 \\ \\ \text{ Although }f(x)=0\text{ is not a positive value, we can include the x\_values corresponding} \\ \text{ to these f\lparen x\rparen values as long as we use open intervals.} \end{gathered}$

Thus, the answer is

$(-2,1)$