F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

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

To find the domain of the function f, we need to consider the given conditions for each part of the function separately:

For the first part, x ≤ 2, there are no restrictions on x, so the domain is (-∞, 2].

For the second part, -2 < x < 0, there are also no restrictions on x, so the domain is (-2, 0).

For the third part, x ≥ 0, there are again no restrictions on x, so the domain is [0, ∞).

Combining all the domains, the overall domain of the function f is (-∞, 2] U (-2, 0) U [0, ∞).

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

To find the range of the function f, we can consider each part of the function separately:

For the first part, f(x) = 3x + 2, when x ≤ 2, the function increases as x increases, so the range is (-∞, f(2)].

f(2) = 3(2) + 2 = 6 + 2 = 8, so the range for the first part is (-∞, 8].

For the second part, f(x) = -0.5x - 3, when -2 < x < 0, the function decreases as x increases, so the range is [f(0), f(-2)).

f(0) = -0.5(0) - 3 = -3, and f(-2) = -0.5(-2) - 3 = 1, so the range for the second part is [-3, 1).

For the third part, f(x) = -5, when x ≥ 0, the function is a constant value, so the range is [-5].

Combining the ranges of each part, the overall range of the function f is (-∞, 8] U [-3, 1) U [-5].

Zeros of the function - to find the zeros of the function, we set f(x) = 0 and solve for x:

For the first part, 3x + 2 = 0, we have:

3x = -2, x = -2/3.

For the second part, -0.5x - 3 = 0, we have:

-0.5x = 3, x = -6.

For the third part, -5 = 0, there are no solutions.

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

Intersection with Oy - to find the point of intersection with the y-axis, we set x = 0 and solve for f(x):

For the first part, f(0) does not exist.

For the second part, f(0) = -0.5(0) - 3 = -3.

For the third part, f(0) = -5.

So, the point of intersection with the y-axis is (0, -3) for the second part and (0, -5) for the third part.

Increasing or decreasing function - to determine if the function is increasing or decreasing, we can look at the slopes of each part of the function:

For the first part, f(x) = 3x + 2, the slope is positive (3), so the function is increasing.

For the second part, f(x) = -0.5x - 3, the slope is negative (-0.5), so the function is decreasing.

For the third part, f(x) = -5, the slope is zero, so the function is neither increasing nor decreasing (constant).

In summary: D(f) = (-∞, 2] U (-2, 0) U [0, ∞), E(f) = (-∞, 8] U [-3, 1) U [-5], zeros of f: x = -2/3, x = -6, intersection with Oy: (0, -3) and (0, -5), the function increases for the first part (x ≤ 2), decreases for the second part (-2 < x < 0), and is constant for the third part (x ≥ 0).