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.

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.

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.

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.

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.

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.

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.

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.