1.3 Rates of Change in Linear & Quadratic Functions
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Horizontales
The________ of a function over an interval of the function’s domain is the constant rate of change that yields the same change in the output values as the function yielded on that interval of the function’s domain. It is the ratio of the change in the output values to the change in input values over that interval.
he graph of a function is concave up on intervals in which the rate of change is increasing.
The input and output values of a function vary in tandem according to a function, which is expressed graphically, numerically, analytically, or verbally.
The AROC over [a,b] is the slope of the secant line from (a , ((a)) to (b , f(b)) .
For linear functions, the AROCs are changing at a rate of zero, since they are constant.
For a quadratic function, The AROCs over consecutive equal-length input-value intervals can be given by a linear function.
A function is increasing over an interval of its domain: If, as the input values increase, the output values always increase. That is: For all a,b within an interval, If a&lt;b, then fa&lt;f(b).
For a linear function, the AROC over any length input-value interval is constant.
The variable representing the input values.
Verticales
A function is decreasing over an interval of its domain: If, as the input values increase, the output values always decrease. That is: For all a,b within an interval, If a&lt;b, then fa&gt;f(b).
For quadratic functions, the AROCs are changing at a constant rate, since they are linear.
The variable representing the output values.
For a linear function, the AROC over any length input-value interval is constant
AVERAGE RATE OF CHANGE
The _____________ of a function at a point quantifies the rate at which output values would change were the input values to change at that point. This rate of change at a point can be approximated by the average rates of change of the function over small intervals containing the point, if such values exist.
The graph of a function is concave down on intervals in which the rate of change is decreasing.
A mathematical relation that maps a set of input values (domain) to a set of output values (range).
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