Horizontal Asymptotes and Initial Values

The video tutorial from KH Academy explains how to graph basic exponential functions. It begins by introducing the concept of exponential functions, highlighting the initial value and common ratio. The tutorial then demonstrates how to graph these functions using a graphing tool, focusing on defining key points and horizontal asymptotes. A second example is provided, illustrating the graphing process with a negative initial value. The video emphasizes understanding the behavior of exponential functions as x approaches infinity or negative infinity.

What is the initial value of the function H(x) = 27 * (1/3)^x?

• 1

• 27

• 1/3

• 9

What is the common ratio in the function H(x) = 27 * (1/3)^x?

• 9

• 3

• 1/3

• 27

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

• 27

• 9

• 3

• 1

What happens to the value of H(x) as x becomes very large?

• It becomes negative

• It approaches 0

• It approaches 27

• It remains constant

What is the horizontal asymptote of the function H(x) = 27 * (1/3)^x?

• y = -27

• y = 1

• y = 0

• y = 27

What is the value of H(x) when x = 2?

• 3

• 1

• 27

• 9

What is the initial value of the function G(x) with a negative initial value?

• 60

• -60

• 30

• -30

What is the value of G(x) when x = 1 for the function with a negative initial value?

• 60

• -30

• -60

• 30

What happens to the value of G(x) as x becomes very negative?

• It approaches 30

• It becomes positive

• It remains constant

• It approaches 0

What is the horizontal asymptote of the function G(x) with a negative initial value?

• y = -60

• y = 30

• y = 0

• y = -30