3.5 ESL Flashcard

Front

What does it mean for a function to be 'never decreasing'?

Back

A function is 'never decreasing' if its value does not decrease as the input increases. This means that for any two points in the domain, if x1 < x2, then f(x1) <= f(x2).

Front

List the types of intervals that a graph can demonstrate.

Back

The types of intervals a graph can demonstrate include increasing, constant, and decreasing.

Front

What does it mean for a function to be 'increasing'?

Back

A function is 'increasing' if, as the input values increase, the output values also increase. This means that for any two points in the domain, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be 'constant'?

Back

A function is 'constant' if its output value does not change as the input value changes. This means that for any two points in the domain, f(x1) = f(x2) for all x.

Front

What does it mean for a function to be 'decreasing'?

Back

A function is 'decreasing' if, as the input values increase, the output values decrease. This means that for any two points in the domain, if x1 < x2, then f(x1) > f(x2).

Front

How can you determine if a function is increasing, constant, or decreasing over an interval?

Back

You can determine this by analyzing the slope of the function over that interval. If the slope is positive, the function is increasing; if the slope is zero, it is constant; and if the slope is negative, it is decreasing.

Front

What does it mean for a distance to 'remain constant' between two points in time?

Back

It means that the distance does not change as time progresses, indicating that the object is not moving during that time interval.

Front

What is the significance of identifying intervals in a graph?

Back

Identifying intervals helps in understanding the behavior of the function, such as where it increases, decreases, or remains constant, which is crucial for analyzing trends and making predictions.

Front

What is the relationship between the slope of a function and its increasing or decreasing nature?

Back

The slope of a function indicates its rate of change. A positive slope indicates the function is increasing, a negative slope indicates it is decreasing, and a zero slope indicates it is constant.

Front

What does it mean for a function to be 'always increasing'?

Back

A function is 'always increasing' if, for every pair of points in its domain, the output value at the higher input is always greater than the output value at the lower input.