F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

To find the domain (D(f)) and the range (E(f)) of the function, we need to consider the intervals where the function is defined.

For f(x) = 3x + 2, x ≤ 2, the function is defined for all x values less than or equal to 2.

For f(x) = -0.5x - 3, -2 < x < 0, the function is defined for all x values between -2 and 0, but not including -2 and 0.

For f(x) = -5, x ≥ 0, the function is defined for all x values greater than or equal to 0.

Therefore, the domain of f(x) is (-∞, 2] for the first part, (-2, 0) for the second part, and [0, ∞) for the third part.

To find the range, we can analyze the slopes of the different parts of the function.

For f(x) = 3x + 2, the slope is positive (3), so the function increases as x increases.

For f(x) = -0.5x - 3, the slope is negative (-0.5), so the function decreases as x increases.

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

Therefore, the range of f(x) is (-∞, ∞) because the function can take any real value.

To find the zeros of the function, we need to find the x-values where f(x) = 0.

For the first part (3x + 2), setting f(x) = 0 gives us 3x + 2 = 0. Solving for x, we get x = -2/3, which is a zero of the function.

For the second part (-0.5x - 3), since the function is a linear equation, there are no zeros.

For the third part (-5), since the function is a constant, there are no zeros.

To find the point of intersection with the y-axis, we need to find the y-value when x = 0.

For the first part (3x + 2), setting x = 0 gives us f(0) = 3(0) + 2 = 2. So the point of intersection with the y-axis is (0, 2).

For the second part (-0.5x - 3), when x = 0, we get f(0) = -0.5(0) - 3 = -3. So the point of intersection with the y-axis is (0, -3).

For the third part (-5), since the function is a constant, the y-value is always -5 regardless of the x-value.

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

In summary: D(f) = (-∞, 2] ∪ (-2, 0) ∪ [0, ∞) E(f) = (-∞, ∞) Zeros of the function: -2/3 Point of intersection with the y-axis: (0, 2), (0, -3), (0, -5) The function increases for the first part (3x + 2), decreases for the second part (-0.5x - 3), and remains constant for the third part (-5).