F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2
To find the domain (D(f)) of the function, we need to determine the values of x for which the function is defined.
From the given information, we have three cases:
f(x) = 3x + 2 for x ≤ 2: In this case, the function is defined for all values of x less than or equal to 2.
f(x) = -0.5x - 3 for -2 < x < 0: Here, the function is defined for all values of x between -2 and 0 (not including -2 and 0).
f(x) = -5 for x ≥ 0: In this case, the function is defined for all values of x greater than or equal to 0.
Combining these three cases, we can say that the domain of the function is: D(f) = {x: x ≤ 2} U {x: -2 < x < 0} U {x: x ≥ 0}
To find the range (E(f)) of the function, we need to determine the set of all possible output values of the function.
Looking at the given equations, we can see that the range of the function (E(f)) is: E(f) = {-5, 3x + 2 for x ≤ 2, -0.5x - 3 for -2 < x < 0}
To find the zeros of the function, we need to find the values of x for which f(x) = 0.
From the given information, we can see that the function does not have any zeros because there is no equation that sets f(x) equal to zero.
To find the point of intersection with the y-axis (also known as the y-intercept), we need to find the value of f(0).
From the given information, we know that f(x) = -5 for x ≥ 0. Therefore, f(0) = -5.
The function is increasing or decreasing depending on the value of the slope (coefficient of x) in each equation.
For the equation f(x) = 3x + 2 when x ≤ 2, we can see that the coefficient of x (which is 3) is positive. This means that the function is increasing for x ≤ 2.
For the equation f(x) = -0.5x - 3 when -2 < x < 0, the coefficient of x (which is -0.5) is negative. This means that the function is decreasing for -2 < x < 0.
For the equation f(x) = -5 for x ≥ 0, there is no x term, so it is a constant function. A constant function is neither increasing nor decreasing.
Therefore, the function is increasing for x ≤ 2, decreasing for -2 < x < 0, and not increasing or decreasing for x ≥ 0.
