Exponential vs Linear Functions!

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. It has a constant rate of change and can be expressed in 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 is 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

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in the y-values divided by the difference in the x-values is the same for any two points on the function.

Tags

CCSS.HSF-LE.A.1B

Front

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

Back

A linear function can be identified from a table of values if the differences between consecutive y-values are constant as the x-values increase.

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 can be identified from a table of values if the ratio of consecutive y-values is constant as the x-values increase.

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 difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, representing the steepness of the line.

Tags

CCSS.8.EE.B.5

Front

What does it mean for a function to be neither linear nor exponential?

Back

A function is neither linear nor exponential if it does not fit the characteristics of either type, such as having a variable rate of change or a non-constant pattern.

Front

What is an example of a linear function?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2