Exponential Functions and Their Properties

The video tutorial introduces exponential models, explaining how repeated multiplication can be represented by functions of the form y = aB^x. It covers the properties of exponential functions, including conditions for a and B, and how to graph them using a table of values. The tutorial distinguishes between exponential growth and decay, providing examples and explaining how to identify them. It also applies these concepts to financial scenarios, demonstrating how exponential models are used to calculate interest and investment growth.

What is the general form of an exponential function?

• y = a/b^x

• y = ax^b

• y = a + bx

• y = ab^x

Which of the following best describes an exponential function?

• A function with no rate of change

• A function with a linear rate of change

• A function with a variable rate of change

• A function with a constant rate of change

Which of the following is NOT a condition for a function to be exponential?

• B must be greater than 0

• B cannot be 1

• A cannot be 0

• A must be greater than 0

What is the domain of an exponential function?

• All negative numbers

• All integers

• All positive numbers

• All real numbers

What is the range of an exponential function when a > 0?

• y is any real number

• y = 0

• y < 0

• y > 0

What is the horizontal asymptote of the graph of an exponential function?

• x = 0

• y = 0

• y = a

• x = a

In the equation y = a * b^x, what does 'a' represent?

• Growth factor

• Decay factor

• Initial value

• Rate of change

In the context of exponential functions, what does the term 'asymptote' refer to?

• The maximum value of the function

• The minimum value of the function

• A line the graph approaches but never touches

• A point where the graph crosses the axis

What is the role of the exponent 'x' in an exponential function?

• It sets the asymptote

• It affects the rate of growth or decay

• It determines the initial value

• It defines the y-intercept

What is the effect of increasing the value of 'a' in y = a * b^x?

• The graph becomes flatter

• The graph becomes steeper

• The graph shifts down

• The graph shifts up