Graph Transformations and Asymptotes

The video tutorial explains how to identify and apply transformations to a graph, focusing on parameters 'a' and 'k'. It covers vertical shifts, reflections about the y-axis, and the impact on asymptotes. The tutorial also discusses how to determine the domain and range of the transformed graph.

What is the initial value of 'a' in the graph transformation discussed?

• 0

• 3

• 1/3

• 1

Where does the graph initially cross the y-axis before any transformations?

• At 3

• At 1/3

• At 0

• At 1

What does the 'up 3' transformation do to the graph?

• Moves it 3 units down

• Moves it 3 units right

• Moves it 3 units up

• Moves it 3 units left

How does the 'up 3' transformation affect the asymptote?

• It moves the asymptote 3 units down

• It moves the asymptote 3 units up

• It reflects the asymptote over the x-axis

• It does not affect the asymptote

What is the new position of the asymptote after the 'up 3' transformation?

• y = 0

• y = 1

• y = 3

• y = -3

What happens to the graph when 'x' is multiplied by a negative inside the function?

• It shifts down

• It reflects over the x-axis

• It reflects over the y-axis

• It shifts up

What is the effect of multiplying by a negative on the outside of the function?

• Shifts right

• Shifts left

• Reflects over the y-axis

• Reflects over the x-axis

What is the domain of the transformed graph?

• 0 to infinity

• Negative infinity to 0

• Negative infinity to infinity

• 3 to infinity

What is the range of the transformed graph?

• Negative infinity to infinity

• 0 to infinity

• Negative infinity to 3

• 3 to infinity

How does the graph behave as it extends to the left?

• It stops at 3

• It continues to negative infinity

• It stops at 0

• It continues to positive infinity