1. The problem is to graph the function $y=(-2x+1)^3-6$. 2. This is a cubic function with a transformation. The base cubic function is $y=x^3$. 3. The function involves a horizontal stretch/compression and flipping because of the $-2x$ inside the cube. 4. The +1 shifts the function horizontally to the right by $\frac{1}{2}$ because it's inside the cube with $x$. 5. The entire cubic is shifted down by 6 units due to the $-6$ outside the cube. 6. To understand the graph shape, analyze intercepts and key points: - When $x=0$, $y=(-2(0)+1)^3-6 = 1^3 - 6 = -5$. - When $x=\frac{1}{2}$, $y=(-2(\frac{1}{2})+1)^3-6 = ( -1+1)^3-6 = 0 - 6 = -6$. - When $x=1$, $y=(-2(1)+1)^3 - 6 = (-2+1)^3 - 6 = (-1)^3 - 6 = -1 - 6= -7$. 7. The function decreases rapidly due to the cube and negative coefficient. Hence, the graph is a cubic curve shifted right by $\frac{1}{2}$ and down by 6, flipped horizontally due to the negative coefficient. Final answer: The function is $y = (-2x+1)^3 - 6$ representing a reflected and translated cubic curve.