Graph Reflections and Transformations

The video tutorial explains how to reflect exponential graphs about the x-axis and y-axis. It covers the changes in coordinates and asymptotes during these reflections. The tutorial provides step-by-step instructions on transforming the equations of the graphs to reflect these changes, ensuring they are in standard form. The video also highlights the symmetry and mirror images created by these reflections.

What is the initial function used in the video to demonstrate reflections?

• f(x) = 2^(x-1) - 3

• f(x) = 2^(x+1) + 3

• f(x) = 2^(x-1) + 3

• f(x) = 3^(x-1) - 2

When reflecting a graph about the x-axis, what happens to the y-coordinates?

• They change sign.

• They are halved.

• They are doubled.

• They remain the same.

What is the effect on the asymptote when reflecting a graph about the x-axis?

• It remains unchanged.

• It moves to the left.

• It is reflected across the x-axis.

• It moves to the right.

How do you transform the equation when reflecting about the x-axis?

• Add 1 to the exponent.

• Multiply the entire function by -1.

• Divide the entire function by 2.

• Subtract 1 from the exponent.

What happens to the x-coordinates when reflecting a graph about the y-axis?

• They are halved.

• They are doubled.

• They change sign.

• They remain the same.

Which part of the graph remains unchanged when reflecting about the y-axis?

• The slope

• The y-intercept

• The x-intercept

• The asymptote

How is the equation transformed when reflecting about the y-axis?

• Subtract 1 from the exponent.

• Add 1 to the exponent.

• Replace y with -y in the function.

• Replace x with -x in the function.

What is the standard form of the equation after reflecting about the y-axis?

• 1/2^(x+1) - 3

• 1/2^(x-1) + 3

• 2^(x-1) - 3

• 2^(-x-1) - 3

What is the effect of a negative exponent on the base in the equation?

• It becomes a fraction.

• It doubles the base.

• It remains unchanged.

• It halves the base.

What must be done if the base of the function is a fraction?

• Write it without brackets.

• Multiply it by 2.

• Divide it by 2.

• Write it in brackets.