Function Basics

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the vertical line test?

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

Evaluate f(t) = -2t^2 + 1 for f(-3).

Back

f(-3) = -2(-3)^2 + 1 = -2(9) + 1 = -18 + 1 = -17.

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, typically in the form f(x) = mx + b.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

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 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

How do you determine if a table represents a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.