Types of Functions FLASHCARD

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the general shape of a quadratic function's graph?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the x-coordinate.

Front

What is the domain of a quadratic function?

Back

The domain of all quadratic functions is all real numbers, represented as (-∞, ∞).

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is the general shape of an exponential function's graph?

Back

The graph of an exponential function increases rapidly (if b > 1) or decreases rapidly (if 0 < b < 1) as x moves away from the y-axis.

Front

What is a hyperbola?

Back

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or equations, typically represented as the difference of distances to two foci being constant.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a quadratic function?

Back

The range of a quadratic function depends on the direction of the parabola: if it opens upwards, the range is [k, ∞) where k is the y-coordinate of the vertex; if it opens downwards, the range is (-∞, k].