Comparing Linear, Exponential, and Quadratic Functions

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 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 the base (a positive real number), and x is the exponent. It shows rapid growth or decay.

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. Its graph is a parabola.

Front

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

Back

A linear function will have a constant rate of change, meaning the difference between consecutive y-values divided by the difference in x-values will be the same.

Front

What does the y-intercept represent in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of f(x) when x = 0.

Front

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

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, leading to a rapid decrease.

Front

How do you determine if a function is exponential from its graph?

Back

An exponential function's graph will show a rapid increase or decrease and will not have a straight line; it will curve upwards (growth) or downwards (decay).

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.