Final answer:
To write the equation of the function whose graph is sketched below, identify the intercepts and the shape of the graph. It seems to be a quadratic function, so use the equation y = a(x - p)(x - q) and substitute the x-intercepts.
Step-by-step explanation:
To write the equation of the function whose graph is sketched below, we need to determine the key features of the graph, including the intercepts and the shape of the graph.
Let's start by identifying the x-intercepts. These are the points where the graph intersects the x-axis. In the given graph, there are two x-intercepts at x = -2 and x = 4.
Next, let's determine the y-intercept. This is the point where the graph intersects the y-axis. In the given graph, the y-intercept is at y = 3.
Based on the shape of the graph, it seems to be a quadratic function. Therefore, the equation of the function can be written as: y = a(x - p)(x - q), where a is a constant and p and q are the x-intercepts.
Substituting the values of the x-intercepts into the equation, we get: y = a(x + 2)(x - 4).