Answer:
Domain: (−∞, ∞) or all real numbers
Range: [7, ∞) or y ≥ 7
Step-by-step explanation:
The domain of a function is all of the function's possible x-values (or inputs), and the range is all of the possible y-values (or outputs).
We are given the quadradic function y = -3x² + 6x + 4. I have graphed this function, see attached.
The domain of a quadratic function is always (−∞, ∞), also known as all real numbers, because quadratic functions extend forever in both directions along the x-axis.
The range depends on the vertex. Here, the vertex of this function is (1, 7). Since the coefficient of the x² value is negative, we know that the graph is concave down. This means that the range will be all y-values less than the y-coordinate of the vertex, which is 7. The range of this equation is [7, ∞). This can also be written as y ≥ 7, depending on what form is needed.
