f) Sketch the graph. Use the graphing tool to graph the equation \( y=-x^{2}+1 \). g) Find the domain and range of the function. What is the domain? Choose the correct answer below and, if necessary, fill in the answer box to complete your answer. A. The domain is (Type an inequality or a compound inequality.) B. The domain is all real numbers.

The equation \( y = -x^{2} + 1 \) represents a downward-opening parabola with its vertex at the point (0, 1). This means it reaches a maximum height (1) at this point and then slopes downwards on both sides. When sketching the graph, you would see the parabola intersect the y-axis at (0, 1) and cross the x-axis when \( y = 0 \), giving the roots at \( x = -1 \) and \( x = 1 \). The domain of the function is all real numbers, which means you can input any value for \( x \). In mathematical notation, that’s expressed as \( (-\infty, +\infty) \). The range, however, is a bit more limited! Since the graph peaks at \( y = 1 \) and descends to \(-\infty\), the range is \( (-\infty, 1] \).