Functions Average Rates of Change

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

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How do you calculate the average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a) where [a, b] is the interval.

Front

What does the graph of a function represent?

Back

The graph of a function represents the relationship between the input values (x-axis) and the output values (y-axis).

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What is the significance of the slope in a linear function?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much the output changes for a unit change in the input.

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What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer.

Front

What is the difference between f(x) and g(x)?

Back

The difference between two functions f(x) and g(x) is given by f(x) - g(x), which results in a new function.

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What is the sum of two functions?

Back

The sum of two functions f(x) and g(x) is given by f(x) + g(x), which results in a new function.

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What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

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What does it mean for a function to be decreasing?

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A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).