EOC Review Function Chartacteristics

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce. For example, the range of the function f(x) = x^2 is [0, +∞) because the output is always non-negative.

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What are relative maximums and minimums in a function?

Back

Relative maximums are points where the function value is higher than the values around it, while relative minimums are points where the function value is lower than the values around it. These points are found at turning points of the graph.

Front

How do you find relative maximums and minimums on a graph?

Back

Relative maximums and minimums can be found at turning points, which are points where the graph changes direction from increasing to decreasing (maximum) or from decreasing to increasing (minimum).

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What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, as the x-values increase, the y-values also increase. This means that for any two points a and b in the interval, if a < b, then f(a) < f(b).

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What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, as the x-values increase, the y-values decrease. This means that for any two points a and b in the interval, if a < b, then f(a) > f(b).

Front

What is a turning point in a function?

Back

A turning point is a point on the graph of a function where the function changes from increasing to decreasing or from decreasing to increasing. These points are often where relative maximums or minimums occur.

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What is the difference between absolute and relative extrema?

Back

Absolute extrema are the highest or lowest points over the entire domain of the function, while relative extrema are the highest or lowest points in a specific interval.

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What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It represents the output value of the function when the input value (x) is zero.

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What does it mean for a function to be positive on an interval?

Back

A function is positive on an interval if all the output values (y-values) are greater than zero for every input value (x) in that interval.

Front

What does it mean for a function to be negative on an interval?

Back

A function is negative on an interval if all the output values (y-values) are less than zero for every input value (x) in that interval.