Exploring Exponential Function Transformations

The video tutorial covers exponential functions and their transformations using variables a, B, H, and K. It explains how these variables affect the graph of an exponential function, including vertical and horizontal stretches and compressions, and shifts. The tutorial provides practical examples and exercises to illustrate these concepts, along with a detailed analysis of graphs, domains, ranges, and asymptotes. The video concludes with a summary of transformations and encourages viewers to apply these concepts to understand exponential functions better.

What does the variable 'a' do to an exponential function?

• Shifts the graph up or down

• Causes a horizontal stretch or compression

• Shifts the graph left or right

• Causes a vertical stretch or compression

If 'a' is greater than 1, what transformation occurs?

• Horizontal stretch

• Vertical stretch

• Vertical compression

• Horizontal compression

What happens to the graph if 'B' is between 0 and 1?

• Vertical compression

• Horizontal stretch

• Horizontal compression

• Vertical stretch

How do you determine the direction of the shift caused by 'H'?

• It is the same as the sign of H

• It is always to the left

• It is always to the right

• It is the opposite of the sign of H

What is the effect of a positive 'K' on the graph?

• Shifts the graph down

• Shifts the graph up

• Causes a vertical stretch

• Causes a horizontal stretch

What is the range of the function if the graph is shifted up by 2 units?

• y > 0

• y < 0

• y > 2

• y < 2

If the graph is shifted to the right by 3 units, what is the value of 'H'?

• 0

• 1

• -3

• 3

What is the asymptote of the function if 'K' is -3?

• y = 3

• y = -3

• y = 1

• y = 0

If 'a' is 5, what type of transformation occurs?

• Vertical stretch by 5

• Vertical compression by 5

• Horizontal stretch by 5

• Horizontal compression by 5

What is the effect of 'B' being 0.4 on the graph?

• Vertical compression by 2.5

• Horizontal compression by 2.5

• Horizontal stretch by 2.5

• Vertical stretch by 2.5