Exponential Functions and Their Properties

The video tutorial explores exponential functions, focusing on the function f(x) = 2^x. It discusses the domain, range, and graphical representation, highlighting the horizontal asymptote and the increasing nature of the function. The tutorial extends the analysis to general exponential functions a^x, explaining that they share similar properties. It also covers the reflection and behavior of functions like 1/a^x, emphasizing their decreasing nature. The session concludes with a summary of key properties and behaviors of exponential functions.

What is the function f(x) = 2^x an example of?

• Linear function

• Quadratic function

• Exponential function

• Logarithmic function

What is the domain of the function f(x) = 2^x?

• Only positive numbers

• Only negative numbers

• All real numbers

• Only integers

What is the range of the function f(x) = 2^x?

• (-∞, ∞)

• (1, ∞)

• (0, ∞)

• (-∞, 0)

For x > 0, how does 2^x compare to 2^0?

• 2^x is equal to 2^0

• 2^x is greater than 2^0

• 2^x is less than 2^0

• 2^x is negative

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

• It approaches infinity

• It approaches 0

• It approaches -infinity

• It remains constant

What is the y-intercept of the function f(x) = 2^x?

• (0, 0)

• (0, 1)

• (1, 1)

• (1, 0)

What is the nature of the function f(x) = 2^x?

• Constant

• Decreasing

• Oscillating

• Increasing

Does the function f(x) = 2^x have any x-intercepts?

• No, it has no x-intercepts

• Yes, at x = 1

• Yes, at x = 0

• Yes, at x = -1

What is the x-intercept of the function f(x) = 2^x?

• (1, 0)

• None

• (0, 1)

• (0, 0)

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

• It approaches 0

• It approaches infinity

• It approaches -infinity

• It remains constant