Linear vs Exponential

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line, while exponential functions have a variable rate of change that increases or decreases multiplicatively, represented by a curve.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = ab^x, where a is the initial value, b is the base (growth factor), 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 difference between consecutive y-values for equal increments in x-values.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

An exponential function will show a constant ratio between consecutive y-values for equal increments in x-values.

Tags

CCSS.HSF-LE.A.1A

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating the starting point of the function.

Tags

CCSS.HSF.LE.B.5

Front

What does the slope represent in a linear function?

Back

The slope represents the rate of change of y with respect to x, indicating how much y increases or decreases for each unit increase in x.

Tags

CCSS.8.EE.B.5

Front

In the context of saving money, how would you represent an initial amount and a regular deposit in a linear function?

Back

The initial amount is represented as the y-intercept, and the regular deposit is represented as the slope.

Tags

CCSS.HSF.LE.B.5

Front

What is a real-world example of an exponential function?

Back

A real-world example of an exponential function is population growth, where the population increases by a percentage over time.

Front

How does the graph of an exponential function behave as x increases?

Back

As x increases, the graph of an exponential function rises rapidly if the base is greater than 1, or approaches zero if the base is between 0 and 1.

Tags

CCSS.HSF-IF.C.7E