AP Precalculus Unit 1 Refresh

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval [a, b] is given by the formula (f(b) - f(a)) / (b - a). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Front

How do you determine where the average rate of change is negative?

Back

To find where the average rate of change is negative, identify intervals where the function decreases. This occurs when f(b) < f(a) for a < b.

Front

What does it mean for the average rate of change to be decreasing?

Back

The average rate of change is decreasing when the slope of the secant line between two points on the graph is getting smaller as you move along the x-axis.

Front

What is a zero of a function?

Back

A zero of a function is a value of x for which f(x) = 0. It represents the x-intercepts of the graph.

Front

What is multiplicity in relation to zeros?

Back

Multiplicity refers to the number of times a particular zero occurs. For example, if a zero has multiplicity 2, the graph touches the x-axis at that point but does not cross it.

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function indicates the highest power of x in the function. It determines the function's end behavior and the maximum number of zeros.

Front

What does it mean for a function to approach infinity as x approaches negative infinity?

Back

If the limit of f(x) as x approaches -∞ is ∞, it means that the function's values increase without bound as x decreases.

Front

How do you find intervals where f(x) < 0?

Back

To find intervals where f(x) < 0, identify the x-values for which the function's graph lies below the x-axis.

Front

What is the difference between increasing and decreasing intervals?

Back

An increasing interval is where the function's values rise as x increases, while a decreasing interval is where the function's values fall as x increases.

Front

What is the relationship between the average rate of change and the graph of a function?

Back

The average rate of change corresponds to the slope of the secant line between two points on the graph, indicating whether the function is increasing or decreasing.