Function Model Selection and Articulation

Front

What is a function family?

Back

A group of functions that share common characteristics and can be represented by similar equations, such as linear, quadratic, or cubic functions.

Front

What is a linear function?

Back

A function that can be graphically represented as a straight line, defined by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A function that can be represented by a parabolic graph, defined by the equation f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is a cubic function?

Back

A function that can be represented by a cubic polynomial, defined by the equation f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants.

Front

What is the perimeter of a rectangle?

Back

The total distance around the rectangle, calculated as P = 2(length + width).

Front

What is the domain of a function?

Back

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 set of all possible output values (y-values) that a function can produce.

Front

What is an example of a real-world situation modeled by a quadratic function?

Back

The path of a projectile, such as a t-shirt thrown into the air, which follows a parabolic trajectory.

Front

How do you determine the appropriate domain for a function?

Back

By identifying the values of the independent variable that make sense in the context of the problem.

Front

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

Back

They determine the shape and position of the parabola, including its width and direction of opening.