Transformations and Logarithmic Functions

The video tutorial reviews mathematical transformations, focusing on reflections, expansions, contractions, and translations. It demonstrates graphing the function y = 2ln(x+1) - 3, starting with the base function y = ln(x). The tutorial explains the properties of logarithmic functions, including vertical asymptotes and key points. It then applies transformations in a step-by-step manner, detailing vertical expansions, horizontal shifts, and vertical shifts, to sketch the final graph.

Which of the following is NOT a type of transformation discussed in the video?

• Translation

• Expansion

• Rotation

• Reflection

What is the base function discussed in the video?

• y = sin(x)

• y = ln(x)

• y = x^2

• y = e^x

What is the vertical asymptote of the base function y = ln(x)?

• y = 1

• y = 0

• x = 1

• x = 0

What is the base of the logarithm used in the function y = ln(x)?

• Base 10

• Base 5

• Base 2

• Base e

What is the value of ln(1) according to the video?

• Infinity

• e

• 0

• 1

Which method is NOT mentioned for sketching the base function y = ln(x)?

• Direct sketching of the log function

• Using its exponential inverse

• Using a quadratic approximation

• Reflecting around y = x

What is the inverse of the function y = ln(x)?

• y = log(x)

• y = e^x

• y = 1/x

• y = x^2

Which transformation is applied first according to the video?

• Reflections

• Translations

• Expansions

• Contractions

What is the effect of a vertical expansion by a factor of two on the point (e, 1)?

• It becomes (e, 0.5)

• It becomes (2e, 1)

• It becomes (e, 2)

• It becomes (e, 1)

What happens to the point (1, 0) during a vertical expansion by a factor of two?

• It moves to (1, 2)

• It moves to (0, 1)

• It moves to (2, 0)

• It remains at (1, 0)