Comparing Linear, Exponential, and Quadratic Functions

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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 function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive number), and x is the exponent. It grows or decays rapidly.

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.

Front

How do 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. The differences in y-values divided by the differences in x-values will be the same.

Front

What is the general shape of a quadratic function when graphed?

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 does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, leading to rapid increases over time.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, leading to rapid decreases over time.

Front

How can you tell if a function is quadratic from its graph?

Back

A quadratic function's graph will have a U-shape (parabola) and will not be a straight line.

Front

What is the difference between linear and quadratic functions in terms of their equations?

Back

Linear functions have a degree of 1 (e.g., y = mx + b), while quadratic functions have a degree of 2 (e.g., y = ax^2 + bx + c).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.