Function Models of Real World Data

Front

What is the average rate of change in 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.

Front

How do you calculate the average rate of change for a data set?

Back

To calculate the average rate of change, use the formula: (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Front

What type of function is characterized by a constant rate of change?

Back

Linear function.

Front

What type of function is characterized by a variable rate of change that increases or decreases exponentially?

Back

Exponential function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

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.

Front

Given f(x) = ax^2 + bx + c, what type of function is this?

Back

Quadratic function.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

How do you determine if a function is linear, quadratic, or exponential from a graph?

Back

Linear functions show a straight line, quadratic functions show a parabolic curve, and exponential functions show a rapid increase or decrease.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.