Question

Form test intervals by using the values for which the ____ or does not exist and the values at which the function is ___. Using the test intervals, determine the sign of the ___. The graph is concave upward if the ____, then the graph is concave downward if the ____.

Answer 1

To form test intervals, identify where the function is undefined and where it is zero. Use these key points to create intervals where the function is positive and negative. The sign of the function determines its concavity.

Step-by-step explanation:

To form test intervals, we need to identify the values where the function does not exist or is undefined. In this case, the function is undefined when there is a vertical asymptote or a division by zero. We also need to determine the values where the function is zero. Using these key points, we can create intervals where the function is positive and negative.

For example, if the function is concave upward, it means the graph is opening upwards like a U shape. In this case, the function is positive above the curve and negative below the curve. Conversely, if the function is concave downward, the graph opens downwards like an upside-down U shape and the function is negative above the curve and positive below the curve.

By identifying these intervals and the sign of the function within each interval, we can analyze the behavior of the function and understand its concavity.