Understanding Graph Transformations

The video tutorial explains how to transform the graph of y = 2^x by first flipping it over the Y-axis to get y = 2^-x, and then shifting it down by five units to obtain y = 2^-x - 5. The tutorial also discusses how to identify the correct graph from multiple choices by analyzing transformations such as flipping and shifting.

What are the two main changes made to the function y = 2^x in the problem?

• Negating the exponent and subtracting five

• Negating the exponent and adding five

• Squaring the exponent and subtracting five

• Doubling the exponent and adding five

What happens to the graph of y = 2^x when the exponent is negated?

• It shifts down

• It flips over the x-axis

• It flips over the y-axis

• It shifts up

When the exponent is negated, what happens to the point (2, 4) on the graph?

• It becomes (2, -4)

• It becomes (-2, -4)

• It becomes (-2, 4)

• It remains (2, 4)

How does subtracting five affect the graph of y = 2^(-x)?

• It shifts the graph up by five units

• It shifts the graph down by five units

• It shifts the graph left by five units

• It shifts the graph right by five units

What is the new y-intercept after the graph is shifted down by five?

• It remains the same

• It is ten units lower

• It is five units higher

• It is five units lower

What is the new horizontal asymptote after the transformation?

• y = 0

• y = 10

• y = 5

• y = -5

What does the asymptote shift indicate about the graph's behavior?

• The graph approaches y = 10

• The graph approaches y = 0

• The graph approaches y = 5

• The graph approaches y = -5

Which graph choice correctly represents the function y = 2^(-x) - 5?

• The graph flipped over the y-axis and shifted down

• The graph flipped over the y-axis and shifted left

• The graph flipped over the x-axis and shifted down

• The graph flipped over the x-axis and shifted left

What mistake did one of the incorrect graph choices make?

• Flipped over the x-axis instead of the y-axis

• Did not flip the graph at all

• Shifted up instead of down

• Shifted right instead of left

Why should we feel confident about the correct graph choice?

• It matches the graph flipped over the x-axis

• It matches the graph we drew

• It matches the original graph

• It matches the graph shifted to the left