Linear vs Exponential 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 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 appears 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 change?

Back

A linear function changes by adding or subtracting a constant value (the slope) for each unit increase in x.

Front

How does an exponential function change?

Back

An exponential function changes by multiplying or dividing by a constant factor for each unit increase in x.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of y with respect to x, represented by 'm' in the equation y = mx + b.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the value of y when x = 0, represented by 'b' in the equation y = mx + b.

Front

What is a characteristic of linear graphs?

Back

Linear graphs have a constant slope and form a straight line.

Front

What is a characteristic of exponential graphs?

Back

Exponential graphs show rapid growth or decay and are curved, not straight.

Front

Give an example of a linear function.

Back

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

Front

Give an example of an exponential function.

Back

An example of an exponential function is y = 3(2^x).