Final answer:
To sketch the graph of the function y = x³ - 6x² + 9x + 1, we need to find the x-intercepts and y-intercepts. Once we have these points, we can plot them on a graph and connect them with a curve.
Step-by-step explanation:
To sketch the graph of the function y = x³ - 6x² + 9x + 1, we can start by finding the x-intercepts and the y-intercept. To find the x-intercepts, we set y to zero and solve for x. To find the y-intercept, we set x to zero and solve for y. Once we have these points, we can plot them on a graph and connect them with a smooth curve.
Now, for x-intercepts:
Set y = 0
0 = x³ - 6x² + 9x + 1
We can solve this equation using either factoring, synthetic division, or a graphing calculator. After finding the x-intercepts, set x to zero to find the y-intercept.
Once we have the x-intercepts and y-intercept, we can plot these points on a graph and connect them with a smooth curve to sketch the graph of the function.
Learn more about Graphing polynomial functions