F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

To find the domain (D) of the function, we need to determine the values of x for which the function is defined.

From the given information, we have:

• For f(x) = 3x + 2, x ≤ 2: This equation is defined for all x that are less than or equal to 2.
• For f(x) = -0.5x - 3, -2 < x < 0: This equation is defined for x values that are between -2 and 0 (excluding both endpoints).
• For f(x) = -5, x ≥ 0: This equation is defined for all x that are greater than or equal to 0.

Combining these, we can say that the domain of the function f(x) is the set of all x such that x ≤ 2, or -2 < x < 0, or x ≥ 0.

Therefore, D(f) = (-∞, 2] ∪ (-2, 0) ∪ [0, +∞).

To find the range (E) of the function, we need to determine the set of all possible output values of the function.

For the equation f(x) = 3x + 2, since the coefficient of x is positive, the function is increasing. This means that as x increases, f(x) also increases. Therefore, the range for this equation is (-∞, +∞).

For the equation f(x) = -0.5x - 3, since the coefficient of x is negative, the function is decreasing. This means that as x increases, f(x) decreases. Therefore, the range for this equation is (-∞, -3).

For the equation f(x) = -5, the range is simply {-5} since the output is constant.

Combining the ranges for all the equations, we can say that the range (E) of the function f(x) is (-∞, -3) ∪ {-5} ∪ (-∞, +∞).

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

For f(x) = 3x + 2, x ≤ 2, setting f(x) = 0 gives: 3x + 2 = 0 3x = -2 x = -2/3

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

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

To find the point of intersection with the y-axis (Oy), we set x = 0 and evaluate f(x).

For f(x) = -5, x ≥ 0, when x = 0: f(0) = -5

Therefore, the point of intersection with the y-axis is (0, -5).

Lastly, the information given about the function being increasing or decreasing allows us to know its behavior.

For f(x) = 3x + 2, x ≤ 2, the function is increasing.

For f(x) = -0.5x - 3, -2 < x < 0, the function is decreasing.

For f(x) = -5, x ≥ 0, the function is constant.

I hope this helps! Let me know if you have any further questions.