Compare Linear, Quadratic, & Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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) = ax² + 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

How can you identify a linear function from its graph?

Back

A linear function will produce a straight line when graphed, with a constant rate of change.

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function will produce a parabolic shape (U-shaped) when graphed, which can open upwards or downwards.

Front

How can you identify an exponential function from its graph?

Back

An exponential function will show rapid growth or decay, producing a curve that increases or decreases sharply.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction it opens.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster increases over time.