Comparing Linear, Exponential, and Quadratic 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 y = 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 y = ab^x, where a is a constant, b is a positive real number, and x is the exponent. It grows rapidly as x increases.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = 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

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

Back

An exponential function will show a constant multiplicative rate of change, meaning the ratio of consecutive y-values will be constant.

Front

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

Back

A quadratic function will have a second difference that is constant when the first differences of the y-values are calculated.

Front

What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What does the graph of an exponential function look like?

Back

The graph of an exponential function rises rapidly and has a characteristic curve that gets steeper as x increases.

Front

What does the graph of a quadratic function look like?

Back

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

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.