Unit 2 - Behaviors of Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function 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 models situations where growth or decay occurs at a rate proportional to the current value.

Front

What is a linear function?

Back

A linear function is a polynomial function of degree one, which can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. It represents a straight line on a graph.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree two, expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0. Its graph can have one or two turning points.

Front

What type of model is represented by the equation x - 2y = 8?

Back

Linear model.

Front

What type of model is represented by the equation y = 3x^2 + 2?

Back

Quadratic model.

Front

What type of model is represented by the equation y = 2^x?

Back

Exponential model.

Front

What is the general form of a quadratic equation?

Back

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

Front

What is the vertex of a parabola represented by a quadratic function?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens. For the function f(x) = ax^2 + bx + c, the vertex can be found at x = -b/(2a).

Front

What is the significance of the slope in a linear function?

Back

The slope (m) in a linear function indicates the rate of change of the function. A positive slope means the function is increasing, while a negative slope means it is decreasing.