Functions Modified

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs, called the domain.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by parentheses containing the input variable, e.g., f(x).

Front

What does it mean for a function to be defined?

Back

A function is defined for a particular input if there is a corresponding output value.

Front

What is the domain of a function?

Back

The domain of a function is 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 range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you evaluate a function at a specific point?

Back

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

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x, meaning it outputs x if x is positive or 0, and -x if x is negative.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = a(x-h)^2 + k is the point (h, k) where the function reaches its maximum or minimum value.

Front

How do you find the minimum or maximum of a quadratic function?

Back

The minimum or maximum value of a quadratic function can be found at the vertex, which occurs at x = -b/(2a) for the standard form ax^2 + bx + c.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and are represented by a straight line, while quadratic functions have a variable rate of change and are represented by a parabola.