{3x+2, x≤2 f(x) = {-0,5x-3, -2

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

In this case, we have three different expressions for f(x), each with a different domain:

1. For 3x+2, the domain is x ≤ 2. This means that the function is defined for all values of x less than or equal to 2.

2. For -0.5x-3, the domain is -2 < x < 0. This means that the function is defined for all values of x between -2 and 0, excluding -2 and 0.

3. For -5, the domain is x ≥ 0. This means that the function is defined for all values of x greater than or equal to 0.

Therefore, the domain of f(x) is (-∞, -2) ∪ (-2, 0) ∪ (0, ∞).

E(f) - The range of the function f(x) is the set of all possible values that the function can take.

For 3x+2, the range is all real numbers.

For -0.5x-3, the range is all real numbers.

For -5, the range is -5.

Therefore, the range of f(x) is (-∞, ∞).

Zeros of the function - Zeros of the function are the values of x for which f(x) = 0.

For 3x+2, f(x) = 0 when 3x + 2 = 0, which gives x = -2/3.

For -0.5x-3, f(x) = 0 when -0.5x - 3 = 0, which gives x = -6.

For -5, f(x) = 0 when -5 = 0, which is not possible.

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

Point of intersection with the y-axis - The point of intersection with the y-axis is the point (0, f(0)).

For 3x+2, f(0) = 2.

For -0.5x-3, f(0) = -3.

For -5, f(0) = -5.

Therefore, the point of intersection with the y-axis is (0, 2) for 3x+2, (-3) for -0.5x-3, and (-5) for -5.

Increasing or decreasing function - To determine if the function is increasing or decreasing, we need to consider the slope of the function.

For 3x+2, the slope is 3, which is positive. Therefore, the function is increasing.

For -0.5x-3, the slope is -0.5, which is negative. Therefore, the function is decreasing.

For -5, the slope is 0, which means the function is constant.

Therefore, the function 3x+2 is increasing, -0.5x-3 is decreasing, and -5 is constant.