Linear or Exponential

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 f(x) = 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 mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

How can you identify a linear situation?

Back

A linear situation can be identified by a constant rate of change, meaning that as one variable increases, the other variable increases by a fixed amount.

Tags

CCSS.HSF-LE.A.1B

Front

How can you identify an exponential situation?

Back

An exponential situation is characterized by a variable that increases by a constant percentage or factor over equal intervals.

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 Ax + By = C, where A, B, and C are constants.

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 and b is the base.

Tags

CCSS.HSF.LE.A.2

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation represents the rate of change of the dependent variable with respect to the independent variable.

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 factor; it indicates how much the quantity increases for each unit increase in x.

Tags

CCSS.HSF-IF.C.8B

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What is a common characteristic of exponential growth?

Back

A common characteristic of exponential growth is that the quantity increases rapidly over time, often doubling in size at regular intervals.

Tags

CCSS.HSF-IF.C.8B