Exponential vs Linear 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 in which an independent variable appears in the exponent. It can be expressed in the form y = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

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

Back

A linear function will show a constant rate of change between the x and y values, resulting in a straight line when graphed.

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 between the y values as x increases, resulting in a curve when graphed.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What does the y-intercept of a linear function represent?

Back

The y-intercept of a linear function is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is y = a * b^x, where 0 < b < 1.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.

Front

What type of function is represented by the equation y = 4^(x+1)?

Back

The equation y = 4^(x+1) represents an exponential function.