Comparing Linear and Exponential Functions

This lesson compares linear and exponential functions, highlighting their behavior on a graph. Key points of intersection are identified, and the values of the functions are compared before, between, and after these points. The lesson concludes with an analysis of long-term growth, demonstrating that exponential functions eventually outgrow linear functions.

What is the initial point of intersection for the linear and exponential functions?

• x = -1, y = 0

• x = 0, y = 1

• x = 1, y = 0

• x = 38, y = 158

How does the exponential function behave to the left of x = -1?

• It remains constant

• It increases rapidly

• It decreases but never goes below zero

• It becomes negative

What is the general trend of the linear function as x decreases past -1?

• It increases

• It decreases

• It remains constant

• It oscillates

Between the points of intersection, which function has a higher value at x = 20?

• Exponential function

• Neither has a value

• Linear function

• Both are equal

What is the second point of intersection for the linear and exponential functions?

• x = 50, y = 200

• x = 0, y = 0

• x = 38, y = 158

• x = 20, y = 100

At what x value does the linear function have a higher value than the exponential function between the points of intersection?

• x = 40

• x = 30

• x = 20

• x = 10

What happens to the linear function as x approaches 50?

• It has a lower y value than the exponential function

• It becomes negative

• It remains constant

• It surpasses the exponential function

In the long run, which function will have a higher value?

• Linear function

• Exponential function

• Neither will have a value

• Both will remain equal

What is the behavior of the exponential function as x increases indefinitely?

• It decreases

• It grows faster than the linear function

• It remains constant

• It becomes negative

What is the key takeaway about the growth of exponential functions compared to linear functions?

• Exponential functions grow faster

• Linear functions grow faster

• Both grow at the same rate

• Neither grows