Increasing/Decreasing Functions

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What is an increasing function?

Back

An increasing function is a function where, as the input (x) increases, the output (f(x)) also increases. This means that for any two points x1 and x2 in the domain, if x1 < x2, then f(x1) < f(x2).

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What is a decreasing function?

Back

A decreasing function is a function where, as the input (x) increases, the output (f(x)) decreases. This means that for any two points x1 and x2 in the domain, if x1 < x2, then f(x1) > f(x2).

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What does it mean for a function to be constant?

Back

A constant function is a function that does not change its value regardless of the input. For any x in the domain, f(x) = c, where c is a constant.

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How can you identify an increasing function on a graph?

Back

An increasing function on a graph will show a slope that rises as you move from left to right. The line or curve will go upwards.

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How can you identify a decreasing function on a graph?

Back

A decreasing function on a graph will show a slope that falls as you move from left to right. The line or curve will go downwards.

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What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It occurs when x = 0.

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What is the maximum height of a function?

Back

The maximum height of a function refers to the highest point on the graph of the function. It is the largest value of f(x) in the given domain.

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

Back

A function that is never decreasing means that it either increases or remains constant throughout its domain. There are no intervals where the function decreases.

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What is the difference between increasing and decreasing intervals?

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Increasing intervals are sections of the graph where the function rises, while decreasing intervals are sections where the function falls.

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How do you determine if a function is increasing or decreasing between two points?

Back

To determine if a function is increasing or decreasing between two points, compare the function values at those points. If f(x1) < f(x2), it is increasing; if f(x1) > f(x2), it is decreasing.