Understanding Exponential Functions and Their Properties

The video tutorial explains how to sketch the graph of an exponential function, f(x) = 2 * 1.5^x, and determine its domain and range. It demonstrates using a calculator to find function values and plot them as ordered pairs on a graph. The tutorial analyzes the graph's behavior, noting that it increases without bound as x increases and approaches zero as x decreases. The domain is all real numbers, and the range is all positive numbers. The video concludes by verifying these properties through graph analysis.

What is the base of the exponential function f(x) = 2 * 1.5^x?

• 1.5

• 2

• x

• 0

Why is the function f(x) = 2 * 1.5^x always increasing?

• Because the base is negative

• Because the base is equal to 1

• Because the base is greater than 1

• Because the base is less than 1

What is the approximate value of f(-2) for the function f(x) = 2 * 1.5^x?

• 3.00

• 2.00

• 1.33

• 0.89

Which x-value corresponds to the function value of 3 in the table?

• -2

• 1

• 2

• 0

What is the ordered pair for x = 0 in the table of values?

• (0, 3)

• (0, 4.5)

• (0, 2)

• (0, 1.33)

How does the graph behave as x decreases?

• It approaches zero but never touches the x-axis

• It becomes negative

• It remains constant

• It increases without bound

What is the domain of the exponential function f(x) = 2 * 1.5^x?

• All real numbers

• Only positive numbers

• Only negative numbers

• Only integers

What is the range of the exponential function f(x) = 2 * 1.5^x?

• Equal to zero

• Less than zero

• Greater than zero

• All real numbers

How can the domain of the function be verified?

• By using a different function

• By analyzing the table of values

• By calculating the function values

• By checking the graph for holes or breaks

What does the graph never do as it moves to the left?

• Remain constant

• Go above the x-axis

• Decrease without bound

• Touch the x-axis