The graph of y=f(x) is the solid black graph below. Which function represents the dotted graph? Answ er y=f(-x)-1 C y=-f(x-1) y=-f(x+1) y=f(-x)+1

Given the details of the picture, we know that the parabola has its vertex at the origin (0,0), opens upwards, and is symmetric about the y-axis. It also passes through the points (-2,4) and (2,4). This information suggests that the parabola is a standard parabola that has been stretched vertically.Step 1: Determine the equation of the original parabola \(y=f(x)\).Since the parabola is symmetric about the y-axis and passes through (-2,4) and (2,4), we can assume that the parabola has the form , where 'a' is a constant that determines the stretch of the parabola.To find 'a', we use one of the points the parabola passes through, for example, (2,4): So the equation of the parabola is .Step 2: Determine which transformation corresponds to the dotted graph.Now we need to determine which of the given functions represents the dotted graph, which is a transformation of the original graph .Option A: \(y=f(-x)-1\)This represents a reflection of the parabola across the y-axis (which does not change the graph since the original parabola is symmetric about the y-axis) followed by a downward shift of 1 unit.Option B: \(y=-f(x-1)\)This represents a reflection of the parabola across the x-axis (making it open downwards) and a horizontal shift to the right by 1 unit.Option C: \(y=-f(x+1)\)This represents a reflection of the parabola across the x-axis (making it open downwards) and a horizontal shift to the left by 1 unit.Option D: \(y=f(-x)+1\)This represents a reflection of the parabola across the y-axis (which does not change the graph since the original parabola is symmetric about the y-axis) followed by an upward shift of 1 unit.Since the original parabola is symmetric about the y-axis, reflecting it across the y-axis will not change its appearance. Therefore, we can eliminate the reflection across the y-axis as a distinguishing transformation. This leaves us with the vertical shifts to consider.The correct transformation must move the graph either up or down. Since the options that include vertical shifts are A and D, and we know that the dotted graph is a transformation of the original graph with a vertical shift, we can determine the correct answer by considering whether the graph is shifted up or down.Given that the transformation is \(y=f(-x)-1\) or \(y=f(-x)+1\), the only difference is the vertical shift. Since the transformation includes a minus sign before the 1 in option A, it indicates a downward shift. Therefore, the correct answer is:Answer: \(y=f(-x)-1\)