Comparing Linear and Exponential Functions

The video tutorial explores the comparison between linear and exponential functions, specifically F(x) = 3^x and H(x) = 3x + 3. It examines their graphs, identifying two points of intersection where the functions are equal. Below the first intersection, the linear function is less than the exponential, while above the second, the exponential grows faster. The tutorial evaluates statements about the functions' values at specific x-values, confirming which are true based on the graph analysis.

What type of function is F(x) = 3^x?

• Linear

• Quadratic

• Exponential

• Logarithmic

How many points of intersection are there between the graphs of F(x) and H(x)?

• None

• Three

• Two

• One

Below the first intersection point, which function has a lower value?

• Cannot be determined

• H(x)

• F(x)

• Both are equal

At x = 0, which function is greater?

• Cannot be determined

• F(x)

• H(x)

• Both are equal

At x = 2, what is the relationship between F(x) and H(x)?

• H(x) is greater

• Both are equal

• Cannot be determined

• F(x) is greater

At x = 3, which function has a higher value?

• Cannot be determined

• H(x)

• F(x)

• Both are equal

At x = 4, which function is greater?

• Cannot be determined

• H(x)

• Both are equal

• F(x)

What happens to the exponential function after the second intersection point?

• It becomes less than the linear function

• It remains equal to the linear function

• It grows faster than the linear function

• It stops growing

Which statement is false regarding the functions at x = 4?

• Cannot be determined

• H(x) is greater than F(x)

• F(x) is greater than H(x)

• Both are equal

What is the general behavior of the exponential function compared to the linear function as x increases?

• It stops growing

• It grows faster

• It grows at the same rate

• It grows slower