End Behavior and Asymptotes of Logarithmic Functions

The video tutorial explores the concept of end behavior in functions, focusing on logarithmic functions. It explains how end behavior describes the behavior of a function as the input values become very large or very small. The tutorial provides examples of log functions, analyzing their graphs and identifying asymptotes. It discusses how transformations like shifts and reflections affect the end behavior of these functions. The video concludes with a complex example, reinforcing the understanding of end behavior in logarithmic functions.

What does the term 'end behavior' refer to in the context of functions?

• The behavior of a function as x approaches positive or negative infinity.

• The behavior of a function as x approaches zero.

• The maximum value of a function.

• The initial value of a function.

In the context of logarithmic functions, what is an asymptote?

• A point where the function is undefined.

• A line that the graph of the function approaches but never touches.

• The maximum value of the function.

• A point where the function crosses the x-axis.

For the function f(x) = 3 + log(7x - 5), what is the new asymptote after transformations?

• x = -5

• x = 3

• x = 5

• x = 0

What happens to f(x) = 3 + log(7x - 5) as x approaches positive infinity?

• f(x) approaches negative infinity.

• f(x) remains constant.

• f(x) approaches zero.

• f(x) approaches positive infinity.

In the function g(x) = 7 - log(4x + 3), what transformation occurs due to the negative sign?

• A shift to the right.

• A reflection across the x-axis.

• A reflection across the y-axis.

• A shift upwards.

For g(x) = 7 - log(4x + 3), what is the new asymptote after transformations?

• x = 7

• x = 3

• x = -3

• x = 0

What is the end behavior of g(x) = 7 - log(4x + 3) as x approaches positive infinity?

• g(x) approaches positive infinity.

• g(x) approaches zero.

• g(x) approaches negative infinity.

• g(x) remains constant.

In the function f(x) = 4 + log(9 - x + 3), what does the negative inside the logarithm indicate?

• A reflection across the x-axis.

• A reflection across the y-axis.

• A shift to the right.

• A shift upwards.

For f(x) = 4 + log(9 - x + 3), what is the new asymptote after transformations?

• x = 4

• x = 3

• x = -3

• x = 0

What is the end behavior of f(x) = 4 + log(9 - x + 3) as x approaches negative infinity?

• f(x) approaches negative infinity.

• f(x) remains constant.

• f(x) approaches zero.

• f(x) approaches positive infinity.