Linear vs Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form 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 an exponential function?

Back

An exponential function is a function in which an independent variable appears in the exponent. It has 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 have a constant rate of change, meaning the difference between consecutive y-values divided by the difference between consecutive x-values is the same.

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 have a constant ratio of consecutive y-values when divided by the previous y-value, indicating that the y-values are increasing or decreasing by a constant factor.

Tags

CCSS.HSF-LE.A.1A

Front

What is the general form of a linear equation?

Back

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

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What is the general form of an exponential equation?

Back

The general form of an exponential equation is y = a(b^x), where a is a constant, b is the base, and x is the exponent.

Tags

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

If a function has a constant increase of 3 for every increase of 1 in x, what type of function is it?

Back

It is a linear function.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

If a function doubles in value for every increase of 1 in x, what type of function is it?

Back

It is an exponential function.

Tags

CCSS.HSF-LE.A.1A