Graphing Exponential Functions: Key Patterns and Techniques

The video tutorial explores exponential functions, starting with basic graphing techniques by plotting points for functions like f(x) = 2^x. It discusses the behavior of exponential graphs with positive and negative exponents, highlighting the concept of asymptotes. The tutorial then examines the impact of changing the base of exponential functions, showing how larger bases lead to faster growth. It also covers fractional bases and how they result in graph flipping. The video concludes with a preview of more advanced graphing techniques.

What is the value of f(x) when x = 0 for the function f(x) = 2^x?

• 0

• 1

• 2

• 4

What is the value of 2^3?

• 4

• 6

• 8

• 10

What does a negative exponent indicate in an exponential function?

• Addition

• Division

• Multiplication

• Flip

What is the value of 2^-2?

• 1/4

• 1/8

• 1/16

• 1/2

Why does the graph of an exponential function never touch the x-axis?

• It has a vertical asymptote

• It has a horizontal asymptote

• It is always increasing

• It is always decreasing

What happens to the value of an exponential function as x approaches negative infinity?

• It approaches zero

• It approaches infinity

• It becomes negative

• It oscillates

How does increasing the base of an exponential function affect its graph?

• It grows slower

• It grows faster

• It becomes negative

• It remains unchanged

What is the value of 3^2?

• 15

• 12

• 9

• 6

What does the function (1/2)^x equal to in terms of exponents?

• 2^x

• 2^-x

• 1/2^-x

• 1/2^x

How does the graph of 2^-x compare to the graph of 2^x?

• It is unchanged

• It is a diagonal flip

• It is a horizontal flip

• It is a vertical flip