24/25 M1 Comparing Functions #1

Front

What is the Average Rate of Change of a function?

Back

The Average Rate of Change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Front

Which type of function has a constant rate of change?

Back

Linear functions have a constant rate of change, represented by a straight line on a graph.

Front

What is a Quadratic function?

Back

A Quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What characterizes an Exponential function?

Back

An Exponential function is of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. It grows or decays rapidly.

Front

How do you determine the x-intercept of a function?

Back

The x-intercept of a function is found by setting f(x) = 0 and solving for x.

Front

What does it mean for a function to have a negative rate of change?

Back

A function has a negative rate of change when its output decreases as the input increases, resulting in a downward slope on the graph.

Front

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

Back

The vertex of a Quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

What is the difference between Average Rate of Change and Instantaneous Rate of Change?

Back

Average Rate of Change measures the change over an interval, while Instantaneous Rate of Change measures the change at a specific point, often found using derivatives.

Front

What is a Linear function's general form?

Back

The general form of a Linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How can you identify a function with a positive and negative rate of change?

Back

A function with both positive and negative rates of change will have sections where it increases and sections where it decreases, typically seen in a Quadratic function.