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.

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What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 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.

Front

What is an exponential function?

Back

An exponential function is a mathematical 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.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the point where the graph changes direction, and it can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.

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What does the term 'domain' refer to in functions?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

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What does the term 'range' refer to in functions?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that result from using the function.

Front

How do you find f(x) for a given function?

Back

To find f(x) for a given function, substitute the value of x into the function's equation and simplify.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a quadratic function has a variable rate of change and graphs as a parabola.

Front

What is the slope of a linear function?

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The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).