F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

To determine the domain (D(f)) of the function f(x), we consider the conditions given in each piece of the function:

f(x) = 3x + 2, x ≤ 2 The domain is all values of x that are less than or equal to 2.

f(x) = -0.5x - 3, -2 < x < 0 The domain is all values of x that are greater than -2 and less than 0.

f(x) = -5, x ≥ 0 The domain is all values of x that are greater than or equal to 0.

Combining these conditions, the domain of f(x) is x ≤ 2, -2 < x < 0, x ≥ 0.

To determine the range (E(f)) of the function f(x), we consider the possible values of f(x) for each piece:

For the first piece, f(x) = 3x + 2, x ≤ 2, the function increases as x increases. Therefore, the range of this piece is all real numbers.

For the second piece, f(x) = -0.5x - 3, -2 < x < 0, the function decreases as x increases. Therefore, the range of this piece is all real numbers.

For the third piece, f(x) = -5, x ≥ 0, the function is constant at -5. Therefore, the range of this piece is -5.

Combining these ranges, the range of f(x) is all real numbers except -5.

The zeros of a function are the values of x where the function equals zero. To find the zeros of f(x), we set it equal to zero and solve for x:

3x + 2 = 0 3x = -2 x = -2/3

Therefore, the zero of f(x) is x = -2/3.

The point of intersection with the y-axis, or the y-intercept, can be found by setting x = 0 in the function:

f(0) = -5

Therefore, the function intersects the y-axis at the point (0, -5).

To determine whether the function is increasing or decreasing, we look at the slope of each piece. The slope of the first piece, 3x + 2, is positive, indicating that the function is increasing. The slope of the second piece, -0.5x - 3, is negative, indicating that the function is decreasing. The third piece, -5, is a constant value, so it is neither increasing nor decreasing.

Therefore, overall, the function f(x) increases for x ≤ 2, and then decreases for -2 < x < 0.