AP Precalculus Unit 1 Review

Front

What is the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a).

Front

How do you calculate the instantaneous rate of change of a function at a point?

Back

The instantaneous rate of change of a function at a point is found using the derivative of the function at that point.

Front

What is the difference between average rate of change and instantaneous rate of change?

Back

The average rate of change is calculated over an interval, while the instantaneous rate of change is calculated at a specific point.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval where x1 < x2, f(x1) < f(x2).

Front

What is concavity in relation to a function's graph?

Back

Concavity refers to the direction in which a function's graph curves. A function is concave up if it opens upwards and concave down if it opens downwards.

Front

How can you determine if a function is concave down on an interval?

Back

A function is concave down on an interval if the average rate of change over equal-length input-value intervals is decreasing.

Front

What does it mean for a function to be positive on an interval?

Back

A function is positive on an interval if its output values (f(x)) are greater than zero for all x in that interval.

Front

How do you find the intervals where a function is greater than zero?

Back

To find the intervals where a function is greater than zero, solve the inequality f(x) > 0 and identify the x-values that satisfy this condition.

Front

What is the significance of the derivative in understanding rates of change?

Back

The derivative of a function at a point gives the instantaneous rate of change of the function at that point.

Front

What is the formula for the average rate of change of a quadratic function?

Back

For a quadratic function f(x) = ax^2 + bx + c, the average rate of change over an interval [x1, x2] is (f(x2) - f(x1)) / (x2 - x1).