Understanding Exponential Functions

The video tutorial explains how to evaluate the function f(x) = 3 * 2^(x + 1) for different values of x, including -2, -1, 0, 1, and 2. It demonstrates the substitution process for each value, simplifies the expressions, and calculates the function values. The tutorial then shows how to plot these values on a graph, forming ordered pairs. It concludes by discussing the domain and range of the function, emphasizing that the function approaches zero but never reaches it, and increases without bound.

What is the value of f(-2) for the function f(x) = 3 * 2^(x + 1)?

• 12

• 3

• 6

• 1.5

When calculating f(-1), what is the simplified result?

• 1.5

• 3

• 6

• 12

What is the value of f(0) for the function f(x) = 3 * 2^(x + 1)?

• 12

• 6

• 3

• 1.5

What is the result of f(1) for the given function?

• 1.5

• 3

• 6

• 12

What is the value of f(2) for the function f(x) = 3 * 2^(x + 1)?

• 18

• 8

• 24

• 12

Which ordered pair corresponds to f(-2)?

• (-2, 1.5)

• (-1, 3)

• (0, 6)

• (1, 12)

What is the ordered pair for f(0)?

• (-2, 1.5)

• (1, 12)

• (-1, 3)

• (0, 6)

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

• It approaches zero but never reaches it.

• It remains constant.

• It becomes negative.

• It intersects the horizontal axis.

What is the domain of the function f(x) = 3 * 2^(x + 1)?

• Only integers

• All real numbers

• All negative numbers

• All positive numbers

What is the range of the function f(x) = 3 * 2^(x + 1)?

• (0, Infinity)

• (-Infinity, Infinity)

• [0, Infinity)

• (-Infinity, 0)