F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

To find the domain (D) of a function, we need to determine the values of x for which the function is defined. Looking at the given function, we can see that it is defined for all real numbers x.

Therefore, the domain of the function f(x) is D(f) = (-∞, ∞).

To find the range (E) of a function, we need to determine the possible values of the function f(x) for the given domain.

For x ≤ 2, the function f(x) = 3x + 2. To find the range for this interval, we can substitute the minimum and maximum values of x in the function.

When x = 2, f(x) = 3(2) + 2 = 8. When x approaches negative infinity, f(x) approaches negative infinity as well. Therefore, the range for x ≤ 2 is (-∞, 8].

For -2 < x < 0, the function f(x) = -0.5x - 3. Again, we can find the range by substituting the minimum and maximum values of x.

When x approaches 0, f(x) approaches -3. When x approaches negative infinity, f(x) approaches positive infinity. Therefore, the range for -2 < x < 0 is (-∞, -3].

For x ≥ 0, the function f(x) = -5. Since the function is constant, the range for x ≥ 0 is {-5}.

Therefore, the range of the function f(x) is E(f) = (-∞, -3] ∪ {-5} ∪ (-∞, 8].

To find the zeros (or x-intercepts) of a function, we set f(x) equal to zero and solve for x.

For the first interval, 3x + 2 = 0. Solving this equation, we find x = -2/3. Therefore, for x ≤ 2, the zero of the function is x = -2/3.

For the second interval, -0.5x - 3 = 0. Solving this equation, we find x = -6. Therefore, for -2 < x < 0, the zero of the function is x = -6.

There are no zeros for x ≥ 0, as the function is a constant -5.

The point of intersection with the y-axis (Oy) is the value of f(0).

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

To determine if the function is increasing or decreasing, we can look at the coefficient of x in each interval.

For x ≤ 2, the coefficient of x is 3, which is positive. Therefore, the function is increasing in this interval.

For -2 < x < 0, the coefficient of x is -0.5, which is negative. Therefore, the function is decreasing in this interval.

For x ≥ 0, the function is constant, so it neither increases nor decreases.

In summary:

• D(f) = (-∞, ∞)
• E(f) = (-∞, -3] ∪ {-5} ∪ (-∞, 8]
• Zeros: x = -2/3 for x ≤ 2, x = -6 for -2 < x < 0
• Intersection with Oy: (0, -5)
• The function f(x) is increasing for x ≤ 2 and decreasing for -2 < x < 0. For x ≥ 0, the function is constant.