Types of Functions

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 a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What is an exponential function?

Back

An exponential function is a 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. Its graph increases or decreases rapidly.

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values.

Front

How can you identify a quadratic function from a table of values?

Back

A quadratic function will show a constant second difference in the y-values when the x-values are equally spaced.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive y-values when the x-values are equally spaced.

Front

What is the general shape of a linear function's graph?

Back

The graph of a linear function is a straight line.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards.