Logarithmic and Exponential Functions

The video tutorial explains the concept of end behavior in mathematical functions, focusing on how functions behave as they approach positive and negative infinity. It covers the analysis of an exponential function with a horizontal asymptote at y=0 and a logarithmic function with a vertical asymptote at x=0. The tutorial demonstrates how to track the behavior of these functions as they move towards infinity, providing insights into their growth and limitations.

What does it mean when x approaches negative infinity?

• The function is approaching zero.

• The function is moving to the right.

• The function is approaching positive infinity.

• The function is moving to the left.

What is the end behavior of a function?

• How the function behaves at the origin

• How the function behaves as x approaches zero

• How the function behaves as x approaches negative and positive infinity

• How the function behaves at its maximum point

What is the horizontal asymptote of the function y = 2^x?

• y = 2

• y = 1

• y = -1

• y = 0

As x approaches negative infinity in the function y = 2^x, what does y approach?

• Negative infinity

• Positive infinity

• Zero

• One

As x approaches positive infinity in the function y = 2^x, what does y approach?

• Zero

• Negative infinity

• One

• Positive infinity

What happens to the function y = 2^x as it moves to the right?

• It goes down

• It stays constant

• It goes up

• It oscillates

What type of asymptote does a logarithmic function have?

• No asymptote

• Diagonal asymptote

• Vertical asymptote

• Horizontal asymptote

Where is the vertical asymptote for the logarithmic function with a base of 2?

• x = 2

• x = -1

• x = 1

• x = 0

As x approaches positive infinity in a logarithmic function, what does y approach?

• Zero

• One

• Negative infinity

• Positive infinity

As x approaches zero in a logarithmic function, what does y approach?

• Positive infinity

• Negative infinity

• Zero

• One