Linear vs Exponential

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has 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 in which an independent variable is in the exponent. It has the form y = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

How does a linear function grow?

Back

A linear function grows at a constant rate. For every unit increase in x, y increases by a fixed amount.

Front

How does an exponential function grow?

Back

An exponential function grows at an increasing rate. As x increases, y increases by a larger and larger amount.

Front

What is the general shape of a linear graph?

Back

The graph of a linear function is a straight line.

Front

What is the general shape of an exponential graph?

Back

The graph of an exponential function is a curve that rises rapidly.

Front

What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of y with respect to x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of y when x is 0.

Front

Can a linear function ever be exponential?

Back

No, a linear function cannot be exponential. They are fundamentally different types of functions.

Front

Give an example of a linear function.

Back

An example of a linear function is y = 2x + 3.