Final answer:
The domain of the equation y = (x+2)(x-3) is all real numbers. The range of the equation is all real numbers less than or equal to -5/2.
Step-by-step explanation:
The given equation is y = (x+2)(x-3). To find the domain and range of this equation, we need to consider the possible values of x and the corresponding values of y.
Domain: The domain of the equation is the set of all possible values of x. Since there are no restrictions on the values of x, the domain is all real numbers.
Range: To find the range, we can graph the equation or analyze the shape of the equation. The equation is a quadratic function, which opens upwards because the coefficient of the x^2 term is positive. Therefore, the minimum value of the function occurs at the vertex of the parabola. The x-coordinate of the vertex is -b/2a, where a and b are the coefficients of the quadratic equation. In this case, a = 1 and b = -1, so the x-coordinate of the vertex is 1/2. Substituting this value into the equation, we get y = (1/2 + 2)(1/2 - 3) = -5/2. Therefore, the range of the equation is all real numbers less than or equal to -5/2.