{3x+2, x≤2 f(x) = {-0,5x-3, -2

D(f) - Domain of the function f

E(f) - Range of the function f

To find the domain of a function, we need to determine the values of x for which the function is defined. In this case, we have three different expressions for the function f(x) depending on the value of x.

For the first expression, 3x + 2, the function is defined for all values of x since there are no restrictions given.

For the second expression, -0.5x - 3, -2 < x < 0, the function is defined for values of x between -2 and 0.

For the third expression, -5, the function is defined for x ≥ 0.

Therefore, the domain of the function f is x ≤ 2.

To find the range of a function, we need to determine the values that the function can take. In this case, the function f(x) takes on different values depending on the value of x.

For the first expression, 3x + 2, there are no restrictions on the values it can take.

For the second expression, -0.5x - 3, -2 < x < 0, the function takes on values less than or equal to -3.

For the third expression, -5, the function takes on the value -5.

Therefore, the range of the function f is (-∞, -3] (-infinity to -3].

To find the zeros of a function, we need to solve the equation f(x) = 0. In this case, we can set each expression equal to zero and solve for x.

For 3x + 2 = 0, we have 3x = -2, so x = -2/3.

For -0.5x - 3 = 0, we have -0.5x = 3, so x = -6.

The third expression, -5, is a constant value and does not have any zeros.

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

To find the point of intersection with the y-axis, we need to find the value of f(0). Substituting x = 0 into the expressions for f(x), we get:

For 3x + 2, f(0) = 3(0) + 2 = 2. For -0.5x - 3, f(0) = -0.5(0) - 3 = -3. For -5, f(0) = -5.

Therefore, the point of intersection with the y-axis is (0, 2) for the expression 3x + 2 and (-3, 0) for the expression -0.5x - 3.

To determine whether the function is increasing or decreasing, we can take the derivative of the function with respect to x. However, since the function is defined piecewise, we need to consider each expression separately.

For the expression 3x + 2, the derivative is simply 3, which is a positive constant. Therefore, the function is increasing for the values of x that satisfy the first expression, x ≤ 2.

For the expression -0.5x - 3, the derivative is -0.5, which is a negative constant. Therefore, the function is decreasing for the values of x that satisfy the second expression, -2 < x < 0.

For the third expression, -5, the function is constant and does not change.

Therefore, the function is increasing for x ≤ 2 and decreasing for -2 < x < 0.