Understanding Linear and Exponential Functions

The video tutorial explains how to fill in missing function values in tables and determine if they represent linear or exponential functions. It highlights the difference between repeated addition (linear) and repeated multiplication (exponential). The first table shows exponential growth with a multiplier of five, while the second table shows exponential decay with a multiplier of one-fourth. The video also demonstrates how to graph these functions, showing exponential growth and decay curves.

What does a pattern of repeated addition in function values indicate?

• An exponential function

• A logarithmic function

• A linear function

• A quadratic function

In the first table, what is the growth factor that confirms the function is exponential?

• 0.5

• 10

• 5

• 2

How can you determine the growth factor in a table of function values?

• By adding the function values

• By subtracting the function values

• By dividing a function value by the previous one

• By multiplying the function values

What is the initial value of f(x) in the first table?

• 5

• 12.5

• 2.5

• 0.5

In the second table, what is the growth factor that confirms the function is exponential?

• 1

• 1/8

• 1/4

• 1/2

What is the initial value of g(x) in the second table?

• 1

• 1/4

• 16

• 4

What type of curve does the graph of f(x) represent?

• Quadratic

• Exponential decay

• Exponential growth

• Linear

What type of curve does the graph of g(x) represent?

• Quadratic

• Exponential decay

• Exponential growth

• Linear

What does it mean if a graph goes uphill from left to right?

• Exponential decay

• Linear function

• Constant function

• Exponential growth

What conclusion can be drawn if neither graph forms a line?

• Both are quadratic functions

• One is linear, one is exponential

• Both are linear functions

• Both are exponential functions