Comparing Linear and Exponential Functions

The video tutorial explores the characteristics of exponential and linear functions, specifically f(x) = 3^x and h(x) = 3x + 3. It examines their graphs, identifying two points of intersection and comparing their values at different points. The tutorial evaluates statements about the functions, confirming which are true based on the graph analysis. The exponential function grows faster than the linear function after the second intersection point.

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

• Quadratic

• Exponential

• Logarithmic

• Linear

How many points of intersection are there between the linear and exponential functions?

• None

• Three

• Two

• One

At x = 0, which function has a greater value?

• f(x) = 3^x

• Cannot be determined

• Both are equal

• h(x) = 3x + 3

Which statement is true about the functions at x = 0?

• Cannot be determined

• Both are equal

• h(x) is greater than f(x)

• f(x) is greater than h(x)

At x = 2, what is the relationship between f(x) and h(x)?

• Cannot be determined

• Both are equal

• f(x) is greater than h(x)

• h(x) is greater than f(x)

At x = 3, which function grows faster?

• Both grow at the same rate

• Cannot be determined

• h(x) = 3x + 3

• f(x) = 3^x

At which x-value do the functions f(x) and h(x) intersect for the second time?

• x = 4

• x = 0

• x = 2

• x = 3

Which function is greater at x = 4?

• Cannot be determined

• f(x) = 3^x

• h(x) = 3x + 3

• Both are equal

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

• It grows faster than the linear function

• It remains equal to the linear function

• It stops growing

• It becomes less than the linear function

What is the behavior of the linear function as x approaches negative infinity?

• It becomes positive

• It remains constant

• It approaches zero

• It becomes negative