Exponential vs Linear 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

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

Back

A linear function will have a constant rate of change between the x-values and y-values. The differences in y-values divided by the differences in x-values will be 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 show a constant multiplicative rate of change. The ratio of consecutive y-values will be constant.

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CCSS.HSF-LE.A.1A

Front

What is the slope in a linear function?

Back

The slope (m) in 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 y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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

Tags

CCSS.HSF.LE.A.2

Front

How does the graph of a linear function look?

Back

The graph of a linear function is a straight line that can slope upwards or downwards depending on the sign of the slope.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How does the graph of an exponential function look?

Back

The graph of an exponential function shows a rapid increase or decrease, forming a curve that gets steeper as x increases.

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CCSS.HSF-IF.C.7E