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elcharly64

Answer:

Positive: (-2,1)

Negative: (-∞,-2) U (1,∞)

Step-by-step explanation:

The graph of the function f(x) is given in the figure. We can see some points like (-2,0), (-1,1), (2,-2), and many others.

Note the second value of each point (the value of y) is positive or negative. When it's positive, the graph is above the x-axis, when it's negative, the graph is below the x-axis. When it's 0, the graph crosses the x-axis.

To find the intervals of x where the function is positive, we only have to look into the zone where the graph is above the x-axis. It can be identified as the interval (-2,1).

Similarly, the function is negative in the interval (-∞,-2) U (1,∞)

The function f(x) is positive in the interval [-2, 1].

The function f(x) is negative the interval (-∞, -2) U (1, ∞).

The positive regions of a function f(x) are those intervals where the function is above the x-axis. It is where the y-values are positive (not zero).

To find the intervals of x where the function is positive,

In the interval [-2, 1] , the function f(x) is positive.

The negative regions of a function f(x) are those intervals where the function is below the x-axis. It is where the y-values are negative (not zero).

In the interval (-∞,-2) U (1,∞) , the function f(x) is negative.

y-values that are on the x-axis are neither positive nor negative. The x-axis is where y = 0.

when y = 0, x = -2, 1

Therefore, the function f(x) is positive in the interval [-2, 1] and negative in the interval (-∞,-2) U (1,∞).

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