Exploring Adding and Subtracting Rational Expressions

The video tutorial covers exponential functions, explaining the difference between exponential growth and decay. It provides examples of graphing these functions, including f(x) = 2^x for growth and f(x) = (1/2)^x for decay. The tutorial also explores exponential growth with different bases, such as f(x) = (5/2)^x, and includes practice problems to reinforce learning.

What determines if an exponential function is showing growth?

• The base is less than one.

• The exponent is negative.

• The base is greater than one.

• The function has no asymptotes.

What is the asymptote of an exponential growth function with base 2?

• y = 1

• y = -1

• y = 0

• x = 0

What happens to the value of an exponential growth function as x approaches infinity?

• Becomes negative

• Approaches zero

• Remains constant

• Approaches infinity

For an exponential function with base 1/2, what is the range?

• y > 0

• y < 0

• y >= 0

• y <= 0

In an exponential decay function, what happens to the function's value as x approaches negative infinity?

• Approaches zero

• Approaches infinity

• Becomes negative

• Remains constant

What is the end behavior of the function f(x) = (1/2)^x as x approaches infinity?

• f(x) approaches infinity

• f(x) becomes negative

• f(x) approaches 0

• f(x) approaches 1

What is the domain of all exponential functions discussed?

• x < 0

• Positive integers only

• x > 0

• All real numbers

What is the y-intercept of the exponential function with base 5/2?

• (0, 0.5)

• (0, 1)

• (0, 2.5)

• (1, 0)

Which of the following is true for the exponential function f(x) = 3^x?

• Its range is y < 0.

• It shows exponential decay.

• Its asymptote is y = 1.

• It shows exponential growth.

For the function f(x) = (2/3)^x, what type of function is it?

• Exponential decay

• Quadratic function

• Exponential growth

• Linear growth