Functions & Rate of Change

Front

What is a function in mathematics?

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.

Front

What distinguishes a linear function from a non-linear function?

Back

A linear function has a constant rate of change and its graph forms a straight line, while a non-linear function does not have a constant rate of change and its graph is not a straight line.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you determine if a function is linear by looking at its graph?

Back

If the graph of the function forms a straight line, then the function is linear.

Front

What is the rate of change in the context of functions?

Back

The rate of change refers to how much the output of a function changes for a given change in the input, often represented as the slope in linear functions.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as 'm' in the equation y = mx + b.

Front

What does it mean for a function to be quadratic?

Back

A quadratic function is a polynomial function of degree 2, which means its highest exponent is 2.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, representing either the maximum or minimum value of the function.

Front

How can you identify a quadratic function from its equation?

Back

A quadratic function can be identified by the presence of the x^2 term in its equation, indicating it is a polynomial of degree 2.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value in a quadratic function determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.