Exponential Functions and Their Properties

The video tutorial explains exponential functions, their properties, and how to graph them. It begins by defining exponential functions and providing examples. It then distinguishes between exponential and non-exponential functions, such as polynomial and constant functions. The tutorial proceeds to demonstrate graphing exponential functions, highlighting the differences between increasing and decreasing functions. Finally, it covers the properties of exponential functions, including domain, range, y-intercept, and asymptotes.

What is the general form of an exponential function?

• y = mx + b

• y = ax^2 + bx + c

• y = log(x)

• y = B^x

Which of the following is NOT an exponential function?

• y = x^3

• y = 5^x

• y = 2^x

• y = 3^x

Why can't a negative base be used in an exponential function?

• It results in a complex number for some exponents.

• It makes the function undefined.

• It results in a constant function.

• It causes the function to be linear.

What happens to the graph of an exponential function when the base is greater than 1?

• The graph increases to the right.

• The graph decreases to the left.

• The graph remains constant.

• The graph decreases to the right.

In the example of graphing y = 2^x, what is the y-value when x = 0?

• 0

• 1

• 2

• 4

What is the domain of an exponential function y = B^x?

• 0 to Infinity

• Negative Infinity to 0

• Negative Infinity to Infinity

• 1 to Infinity

What is the range of an exponential function y = B^x?

• 0 to Infinity

• 1 to Infinity

• Negative Infinity to Infinity

• Negative Infinity to 0

Where does the graph of an exponential function cross the y-axis?

• At y = x

• At y = 0

• At y = 1

• At y = B

What is a horizontal asymptote of the function y = B^x?

• y = 0

• y = 1

• x = 0

• x = 1

What property of exponential functions allows them to have an inverse?

• They are one-to-one functions.

• They are polynomial functions.

• They are linear functions.

• They are constant functions.