F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

D(f) - The domain of function f is the set of all possible values of x for which the function is defined.

In this case, the domain of f consists of three intervals:

1. For x ≤ 2, the function is defined.
2. For -2 < x < 0, the function is defined.
3. For x ≥ 0, the function is defined.

Therefore, the domain of f is (-∞, 2], (-2, 0), [0, ∞).

E(f) - The range of function f is the set of all possible values of f(x) for all x in the domain.

By examining each expression for f(x), we can see that f(x) can take on the following values:

1. For x ≤ 2, f(x) is a linear function with a positive slope. Therefore, as x increases, f(x) increases. The range of f in this interval is (-∞, ∞).
2. For -2 < x < 0, f(x) is a linear function with a negative slope. Therefore, as x increases, f(x) decreases. The range of f in this interval is (-∞, -3.5).
3. For x ≥ 0, f(x) is a constant function with a value of -5. Therefore, the range of f in this interval is {-5}.

Therefore, the range of f is (-∞, -3.5) ∪ {-5}.

Zeros of the function: To find the zeros of a function, we need to solve the equations f(x) = 0.

1. For f(x) = 3x + 2, x ≤ 2: 3x + 2 = 0 3x = -2 x = -2/3

2. For f(x) = -0.5x - 3, -2 < x < 0: -0.5x - 3 = 0 -0.5x = 3 x = -6

3. For f(x) = -5, x ≥ 0: Since f(x) is a constant function, it does not have any zeros.

Therefore, the zeros of the function f are x = -2/3 and x = -6.

Point of intersection with Oy (the y-intercept): The point of intersection with Oy can be found by evaluating f(0) for each expression of f(x).

1. For x ≤ 2, f(x) = 3x + 2: f(0) = 3(0) + 2 f(0) = 2 Therefore, the point of intersection with Oy is (0, 2).

2. For -2 < x < 0, f(x) = -0.5x - 3: f(0) = -0.5(0) - 3 f(0) = -3 Therefore, the point of intersection with Oy is (0, -3).

3. For x ≥ 0, f(x) = -5: f(0) = -5 Therefore, the point of intersection with Oy is (0, -5).

Therefore, the function f intersects with the Oy axis at (0, 2), (0, -3), and (0, -5).

Whether the function is increasing or decreasing:

1. For x ≤ 2, f(x) = 3x + 2: The slope of the function is positive (3), so the function is increasing.

2. For -2 < x < 0, f(x) = -0.5x - 3: The slope of the function is negative (-0.5), so the function is decreasing.

3. For x ≥ 0, f(x) = -5: The function is constant, so it neither increases nor decreases.

Therefore, the function f is increasing for x ≤ 2, decreasing for -2 < x < 0, and neither increasing nor decreasing for x ≥ 0.