Families of Functions Flashcard

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

To evaluate a function at a specific point, substitute the value of the variable into the function's equation and simplify.

The general form of a linear function is $$f(x) = mx + b$$ , where m is the slope and b is the y-intercept.

An exponential function is characterized by a constant base raised to a variable exponent, typically in the form $$f(x) = a \times b^x$$ , where a is a constant and b > 0.

To find the y-intercept of a function, set $$x = 0$$ in the function's equation and solve for $$f(0)$$ .

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

A function is decreasing on an interval if, as the input values increase, the output values decrease.

The vertex of a quadratic function in the form $$f(x) = ax^2 + bx + c$$ can be found using the formula $$x = -\frac{b}{2a}$$ .

A function is linear if it describes a constant rate of change, such as a fixed fee per unit or a consistent increase or decrease.

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.