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 = ab^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x = 0.

Front

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

Back

A linear function will have a constant rate of change; the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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 multiplicative rate of change; the ratio of consecutive y-values will be the same.

Tags

CCSS.HSF-LE.A.1A

Front

What is the graph of a linear function like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Tags

CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What is the graph of an exponential function like?

Back

The graph of an exponential function shows rapid growth or decay, typically curving upwards or downwards.

Tags

CCSS.HSF-IF.C.7E

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.