Identify Characteristics of Functions

Front

What is a function?

Back

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

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

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it assigns different outputs to different inputs, meaning no two inputs have the same output.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b.

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.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What is a constant function?

Back

A constant function is a function that always returns the same value regardless of the input, typically in the form f(x) = c.

Front

What is a function's intercept?

Back

The intercepts of a function are the points where the graph intersects the axes; the x-intercept is where y=0, and the y-intercept is where x=0.