91Ó°ÊÓ

The function given is \(f(x)=x^4-2x^2+8\). This function is a polynomial function of degree 4 and its domain is the whole set of real numbers (since there are no restrictions on possible values of \(x\)).

Since we want to plot the function within the standard viewing window and the specified window, we need to calculate the values (outputs) of the function within these windows. (a) For the standard viewing window, we typically use the interval \([-10, 10]\) for the \(x\)-axis, and a suitable interval for the \(y\)-axis (we will adjust it according to the outputs of our function in this range). Calculate the values of the function for various points in the interval \([-10,10]\): (b) The specified window for the \(x\)-axis is given as \([-2, 2]\). Similarly, for the \(y\)-axis, the interval is given as \([6, 10]\). Calculate the values of the function for various points in the interval \([-2, 2]\):

Now that we have the calculated values of the function within both windows, we can proceed to plot the graphs. (a) Standard viewing window: Plot the graph on a grid with the \(x\)-axis interval: \([-10, 10]\). The \(y\)-axis interval should be adjusted to accommodate the appropriate values of the function, but the graph should at least cover the \([-10, 10]\) interval for the \(x\)-axis. (b) Specified window: Plot the graph on a grid with the \(x\)-axis interval: \([-2, 2]\) and the \(y\)-axis interval: [6, 10]. Connect these points according to the calculated values of the function. Remember to label the axes and indicate the coordinates of any critical points (such as turning points, intercepts, etc.) on the graph, to make it complete and clear. After following these steps, you will have successfully plotted the graph of the function \(f(x) = x^4 - 2x^2 + 8\) within the standard viewing window and the specified window \([-2, 2] \times [6, 10]\).