Function Family Review

Front

What is the defining characteristic of a quadratic function?

Back

A quadratic function is defined by the presence of a variable raised to the second power, typically in the form f(x) = ax^2 + bx + c.

Front

What type of function is represented by a straight line on a graph?

Back

A linear function is represented by a straight line on a graph, characterized by a constant rate of change.

Front

What is a key feature of a linear function regarding variables?

Back

A linear function can be defined without a variable, such as in the case of a constant function.

Front

What is the general form of a linear function?

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

What is the defining characteristic of an exponential function?

Back

An exponential function is characterized by a constant base raised to a variable exponent, typically in the form f(x) = a * b^x.

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function's graph is a parabola, which can open upwards or downwards depending on the sign of the leading coefficient.

Front

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

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of f(0).

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.