F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

D(f) - The domain of function f, refers to the set of all possible values of x for which the function is defined. In this case, we need to find the values of x for which each piece of the function is defined:

1. For the first piece of the function, f(x) = 3x + 2, x ≤ 2. This means that x can take any value less than or equal to 2.

2. For the second piece of the function, f(x) = -0.5x - 3, -2 < x < 0. This means that x can take any value between -2 and 0, excluding -2 and 0.

3. For the third piece of the function, f(x) = -5, x ≥ 0. This means that x can take any value greater than or equal to 0.

Putting all these conditions together, we find that the domain of f is:

D(f) = x ≤ 2, -2 < x < 0, x ≥ 0

E(f) - The range of function f refers to the set of all possible values of f(x) for all values of x in the domain. To find the range, we need to consider the values that f(x) can take for each piece of the function:

1. For the first piece of the function, f(x) = 3x + 2, x ≤ 2. As x can take any value less than or equal to 2, f(x) can take any value greater than or equal to 2.

2. For the second piece of the function, f(x) = -0.5x - 3, -2 < x < 0. As x can take any value between -2 and 0, excluding -2 and 0, f(x) can take any value between -2 and -3.

3. For the third piece of the function, f(x) = -5, x ≥ 0. As x can take any value greater than or equal to 0, f(x) is always -5.

Putting all these conditions together, we find that the range of f is:

E(f) = f(x) ≥ 2, -3 ≤ f(x) ≤ -2

Now let's find the zeros of the function, which are the values of x for which f(x) = 0:

1. For the first piece of the function, f(x) = 3x + 2, x ≤ 2. To find the zero, we need to solve the equation 3x + 2 = 0. This gives x = -2/3. However, since x can only take values less than or equal to 2, there are no zeros for this piece of the function.

2. For the second piece of the function, f(x) = -0.5x - 3, -2 < x < 0. To find the zero, we need to solve the equation -0.5x - 3 = 0. This gives x = -6. However, since x can only take values between -2 and 0, excluding -2 and 0, there are no zeros for this piece of the function.

3. For the third piece of the function, f(x) = -5, x ≥ 0. Since f(x) is always -5 for x greater than or equal to 0, there are no zeros for this piece of the function.

Therefore, there are no zeros for the given function.

Next, let's find the point of intersection with the y-axis, which is the value of f when x = 0:

For the third piece of the function, f(x) = -5, x ≥ 0. When x = 0, f(x) = -5.

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

Finally, let's determine whether the function is increasing or decreasing:

1. For the first piece of the function, f(x) = 3x + 2, x ≤ 2. This is a linear function with a positive slope of 3, which means that it is increasing.

2. For the second piece of the function, f(x) = -0.5x - 3, -2 < x < 0. This is also a linear function with a negative slope of -0.5, which means that it is decreasing.

3. For the third piece of the function, f(x) = -5, x ≥ 0. Since f(x) is constant and does not change with respect to x, it is neither increasing nor decreasing.

Therefore, the function is increasing for x ≤ 2, decreasing for -2 < x < 0, and neither increasing nor decreasing for x ≥ 0.