Sketch the graph of y = x5 – x4 + 6x2 – 2, labelling the y-intercept

To sketch the graph of the function y = x^5 - x^4 + 6x^2 - 2, follow these steps:

1. Identify the y-intercept: The y-intercept is the value of y when x = 0. Substituting x = 0 into the equation gives y = 0^5 - 0^4 + 6*0^2 - 2 = -2. So the y-intercept is -2.

2. Identify the x-intercepts: The x-intercepts are the values of x when y = 0. Setting y = 0 gives the equation 0 = x^5 - x^4 + 6x^2 - 2. Solving this equation for x can be complex and may require numerical methods or graphing software.

3. Identify the behavior at the ends of the graph: As x approaches positive infinity, the x^5 term will dominate, so y will approach positive infinity. As x approaches negative infinity, the x^5 term will still dominate, but since the power is odd, y will approach negative infinity.

4. Sketch the graph: Start by plotting the y-intercept at (0, -2). Then, plot the x-intercepts if they were found. Finally, sketch the ends of the graph going towards positive infinity on the right and negative infinity on the left. The exact shape of the graph in the middle will depend on the x-intercepts and may require additional points to be plotted for accuracy.

Please note that this is a rough sketch and the exact shape may vary. For a precise graph, use graphing software or a graphing calculator.