Linear vs Exponential

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What is the general form of a linear function?

Back

The general form of a linear function is 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 the general form of an exponential function?

Back

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

Front

How does the graph of a linear function look?

Back

The graph of a linear function is a straight line.

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 is a curve that increases or decreases rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

A constant rate of change means that for every unit increase in x, the value of y increases or decreases by a fixed amount.

Tags

CCSS.HSF-LE.A.1B

Front

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

Back

A variable rate of change means that the amount by which y changes for each unit increase in x is not constant; it changes depending on the value of x.

Tags

CCSS.HSF-LE.A.1B

Front

In the context of the quiz, what does 'decay' refer to in an exponential function?

Back

Decay in an exponential function refers to a decrease in value over time, often represented by a base less than 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the rate of change for a linear function?

Back

The rate of change for a linear function is constant and is represented by the slope (m) in the equation y = mx + b.

Tags

CCSS.HSF-LE.A.1B