1. The problem is to plot the graph of the function $$y = 4x^4 + 6$$ and analyze the given points $(-1,10)$, $(1,6)$, $(1,10)$, $(2,70)$, and $(3,330)$. 2. The function is a polynomial of degree 4, which means it is symmetric and grows quickly for large values of $x$. 3. To verify the points, substitute each $x$ value into the function and calculate $y$. 4. For $x = -1$: $$y = 4(-1)^4 + 6 = 4(1) + 6 = 10$$ which matches the point $(-1,10)$. 5. For $x = 1$: $$y = 4(1)^4 + 6 = 4(1) + 6 = 10$$ so the point $(1,10)$ is correct, but $(1,6)$ is not on the curve. 6. For $x = 2$: $$y = 4(2)^4 + 6 = 4(16) + 6 = 64 + 6 = 70$$ which matches the point $(2,70)$. 7. For $x = 3$: $$y = 4(3)^4 + 6 = 4(81) + 6 = 324 + 6 = 330$$ which matches the point $(3,330)$. 8. The point $(1,6)$ does not lie on the curve defined by the equation. 9. The function is plotted as $$y = 4x^4 + 6$$ which is a smooth curve with a minimum at $x=0$ where $y=6$.