Final answer:
To determine the positive and negative intervals of a function using a graphing calculator like the TI-83, 83+, or 84, you can graph the function, utilize the 'Trace' feature to find x-intercepts and observe sign change.
Step-by-step explanation:
To determine the positive and negative intervals of a function using a calculator, you can generally follow Solution B, which involves using the graphing functions of calculators like the TI-83, 83+, or 84. These calculators have features that allow you to visualize the graph of the function, identify x-intercepts, maximums, and minimums, and examine the sign of the function on specific intervals.
Firstly, enter the function into the calculator and use the graphing feature to plot the function. Once you have the graph, you can use the 'Trace' function to move along the graph and observe where the function values transition from positive to negative and vice versa. These transitions typically occur at x-intercepts, which are points where the graph crosses the x-axis. By doing so, you can map out the intervals on the x-axis where the function is positive (above the x-axis) or negative (below the x-axis).
To check the intervals around critical points, such as maximums, minimums, and intercepts, you can select points on either side of these features and evaluate the function's value to determine the sign on that interval. This process must be repeated across the domain of interest to delineate all the positive and negative intervals of the function.