Exponential Functions and Their Properties

The video tutorial explains how to graph the exponential function f(x) = 0.5^x, convert decimals to fractions, calculate function values, plot points, and analyze the graph's behavior. It also covers the domain and range of the function, emphasizing that the graph decreases as x increases and approaches zero but never becomes negative.

What is the base of the exponential function f(x) = 0.5^x when expressed as a fraction?

• 1/2

• 2

• 1/3

• 3

What is the function value of f(x) when x = -3?

• 0.5

• 1

• 8

• 4

What is the function value of f(x) when x = 1?

• 0.25

• 2

• 1

• 0.5

Which ordered pair corresponds to x = 0?

• (0, 1)

• (0, 4)

• (0, 2)

• (0, 0.5)

Which of the following is NOT an ordered pair from the function values?

• (-2, 4)

• (-3, 8)

• (2, 0)

• (1, 12)

How does the graph of the function behave as x increases?

• It increases without bound

• It becomes negative

• It remains constant

• It approaches zero

What happens to the function values as x decreases?

• They become zero

• They remain constant

• They decrease without bound

• They increase without bound

Which statement is true about the graph of f(x) = 0.5^x?

• It crosses the x-axis

• It never touches the x-axis

• It is a straight line

• It is a parabola

What is the domain of the function f(x) = 0.5^x?

• All positive numbers

• All negative numbers

• All real numbers

• Only integers

What is the range of the function f(x) = 0.5^x?

• Only integers

• All negative numbers

• All positive numbers

• All real numbers