8.6.5 HOMEWORK - Increasing and Decreasing Functions

Front

What is an increasing function?

Back

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

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, where x1 < x2, the function value at x1 is greater than the function value at x2 (f(x1) > f(x2)).

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has the same output for every input (f(x) = c, where c is a constant).

Front

What does the slope (m) in the equation y = mx + b represent?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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What does the y-intercept (b) in the equation y = mx + b represent?

Back

The y-intercept (b) is the point where the line crosses the y-axis (when x = 0).

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How can you determine if a function is increasing or decreasing from its graph?

Back

If the graph rises as you move from left to right, the function is increasing. If it falls, the function is decreasing.

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What is the definition of an interval in mathematics?

Back

An interval is a range of values between two endpoints, which can be open (not including endpoints) or closed (including endpoints).

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What is the notation for an open interval?

Back

An open interval is denoted as (a, b), meaning it includes all numbers between a and b, but not a and b themselves.

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What is the notation for a closed interval?

Back

A closed interval is denoted as [a, b], meaning it includes all numbers between a and b, including a and b.

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What is the difference between increasing and decreasing intervals?

Back

Increasing intervals are ranges where the function's output rises, while decreasing intervals are ranges where the function's output falls.