Integrated 1 Unit 3: Features of a Function

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the output value at the second point is greater than the output value at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the output value at the second point is less than the output value at the first point.

Front

How do you identify increasing intervals on a graph?

Back

Increasing intervals can be identified by looking for sections of the graph where the slope is positive (the graph rises as you move from left to right).

Front

How do you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified by looking for sections of the graph where the slope is negative (the graph falls as you move from left to right).

Front

What is the notation for intervals?

Back

Intervals are expressed using parentheses and brackets: parentheses ( ) indicate that the endpoint is not included, while brackets [ ] indicate that the endpoint is included.

Front

What is the interval notation for the set of all real numbers?

Back

The interval notation for all real numbers is (-∞, ∞).

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined. They help identify where the function changes from increasing to decreasing or vice versa.

Front

How do you find the intervals of increase and decrease using derivatives?

Back

To find intervals of increase and decrease, take the derivative of the function, set it to zero to find critical points, and test intervals around those points.

Front

What is a local maximum?

Back

A local maximum is a point on the graph of a function where the function value is higher than the values of the function at nearby points.