1.2 Increasing/Decreasing Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of x-values where the function's output (y-values) is rising as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of x-values where the function's output (y-values) is falling as x increases.

Front

How do you determine the increasing and decreasing intervals of a function?

Back

To determine increasing and decreasing intervals, analyze the first derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What does the range of a function represent?

Back

The range of a function represents all possible output values (y-values) that the function can produce.

Front

How can you find the range of a function graphically?

Back

Graphically, the range can be found by identifying the lowest and highest points on the graph and determining the y-values covered.

Front

What is the significance of the notation (-∞, a) in interval notation?

Back

The notation (-∞, a) indicates all real numbers less than 'a', extending indefinitely to the left on the number line.

Front

What does the notation [a, b) signify in interval notation?

Back

The notation [a, b) signifies that 'a' is included in the interval (closed), while 'b' is not included (open), covering all numbers between 'a' and 'b'.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints.

Front

What is the first derivative test?

Back

The first derivative test is a method used to determine local maxima and minima of a function by analyzing the sign of the first derivative.

Front

What does it mean for a function to have a range of [1, ∞)?

Back

A range of [1, ∞) means that the function's output values start at 1 and extend indefinitely upwards, including 1 but not having an upper limit.