Understanding End Behavior of Exponential Functions

The video tutorial explains the concept of end behavior in exponential functions, focusing on how the function behaves as x approaches positive and negative infinity. Two examples are provided: one with a function that grows as x approaches positive infinity and approaches a horizontal asymptote as x approaches negative infinity, and another with a function that decays as x approaches positive infinity and grows negatively as x approaches negative infinity. Graphical analysis is used to verify these behaviors.

What does the end behavior of a function describe?

• The slope of the function at any point

• The value of the function as x approaches positive or negative infinity

• The maximum value of the function

• The value of the function as x approaches zero

As x approaches positive infinity for the function f(x) = 3 * 2^x - 10, what happens to the function values?

• They remain constant

• They increase without bound

• They approach zero

• They decrease without bound

What is the horizontal asymptote of the function f(x) = 3 * 2^x - 10 as x approaches negative infinity?

• y = 10

• y = 3

• y = 0

• y = -10

As x approaches positive infinity for the function f(x) = -2 * 0.5^x + 5, what do the function values approach?

• 0

• 5

• -5

• -2

What is the horizontal asymptote of the function f(x) = -2 * 0.5^x + 5 as x approaches positive infinity?

• y = -2

• y = -5

• y = 0

• y = 5

What happens to the value of 0.5 raised to a higher exponent as x approaches positive infinity?

• It gets smaller

• It becomes negative

• It remains constant

• It gets larger

As x approaches negative infinity for the function f(x) = -2 * 0.5^x + 5, what happens to the function values?

• They approach zero

• They decrease without bound

• They increase without bound

• They remain constant

What is the behavior of a fraction raised to a negative exponent as the exponent gets smaller?

• The value gets larger

• The value gets smaller

• The value remains constant

• The value becomes zero

What is the significance of a horizontal asymptote in the context of end behavior?

• It indicates the maximum value of the function

• It is the point where the function crosses the x-axis

• It shows the value the function approaches as x goes to infinity

• It represents the slope of the function

Why is it recommended to analyze the graph when in doubt about end behavior?

• To find the maximum value

• To determine the slope

• To visually confirm the behavior

• To calculate the derivative