Reflections Across Axes: A Deep Dive

The video tutorial by Mr. Banker explains the concept of reflections across the x-axis, y-axis, and origin using points and graphs. It begins with reflecting a point (3,3) across different axes and then extends the concept to functions. The tutorial provides examples of reflecting a function across the x-axis and y-axis, demonstrating the changes in equations and graphing the results to show the mirror images.

What happens to the y-coordinate when a point is reflected over the x-axis?

• It remains unchanged

• It becomes negative

• It doubles in value

• It changes sign

When reflecting a point over the y-axis, what change occurs to the x-coordinate?

• It becomes positive

• It changes sign

• It remains the same

• It becomes zero

What does reflecting a point over the x-axis do to the x-coordinate?

• It becomes negative

• It remains unchanged

• It is squared

• It is halved

After reflecting a point over the y-axis, what happens to the y-coordinate?

• It changes sign

• It remains unchanged

• It becomes negative

• It is doubled

What is the result of reflecting a point across both the x-axis and y-axis?

• Only the x-coordinate changes sign

• The point returns to its original position

• Both coordinates change sign

• Both coordinates become positive

What is the new position of a point after reflecting it around the origin?

• (-y, -x)

• (x, y)

• (-x, -y)

• (y, x)

How do you reflect a graph across the x-axis?

• Multiply the function by -1

• Square the function

• Negate the x-values

• Add 1 to the function

To reflect a graph across the x-axis, you must:

• Negate the y-values in the function

• Multiply the entire function by -1

• Divide the function by -1

• Replace x with -x in the function

What is the effect of reflecting a function across the y-axis?

• The x-values are negated

• The x-values are squared

• The function is divided by -1

• The y-values are negated

Reflecting a graph across the y-axis involves:

• Adding -1 to each x-value

• Negating the y-values

• Multiplying the function by -1

• Replacing x with -x