11/19 - Linear vs Exponential Tables

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, represented by a straight line on a graph. Exponential functions have a variable rate of change, increasing or decreasing at an increasing rate, represented by a curve.

Front

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

Back

A linear function will show a constant difference between consecutive y-values as the x-values increase.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive y-values as the x-values increase.

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

If a table starts with a y-value of 10 and each subsequent y-value is multiplied by 2, what type of function is represented?

Back

Exponential function.

Front

What does it mean for a function to be linear?

Back

A linear function means that the relationship between the independent variable (x) and the dependent variable (y) can be represented by a straight line.

Front

What does it mean for a function to be exponential?

Back

An exponential function means that the relationship between the independent variable (x) and the dependent variable (y) involves a constant multiplicative rate of change.

Front

Can a function be both linear and exponential?

Back

No, a function cannot be both linear and exponential; they represent different types of relationships.

Front

What is a common real-world example of a linear function?

Back

A common example of a linear function is calculating the total cost of items at a fixed price.