Reflecting Functions: Key Concepts and Techniques

The video tutorial explores the concept of function reflection using the Desmos graphing calculator. It demonstrates how to reflect functions over the x-axis, y-axis, and both axes using simple and complex functions. The tutorial explains the mathematical reasoning behind these transformations and encourages viewers to experiment with Desmos to build intuition.

What is the primary tool used in this tutorial for graphing functions?

• WolframAlpha

• GraphCalc

• GeoGebra

• Desmos

What happens to the graph of a function when a negative sign is placed in front of the entire function?

• It shifts up

• It shifts down

• It reflects over the y-axis

• It reflects over the x-axis

If you replace x with -x inside the function, what transformation occurs?

• Reflection over the x-axis

• Vertical shift

• Horizontal shift

• Reflection over the y-axis

What is the result of applying both a negative sign outside the function and replacing x with -x inside the function?

• No transformation

• Reflection over both axes

• Reflection over the y-axis

• Reflection over the x-axis

Why does placing a negative sign in front of a function reflect it over the x-axis?

• It changes the sign of the x-values

• It shifts the graph horizontally

• It changes the sign of the y-values

• It shifts the graph vertically

What happens to the function e^x when you replace x with -x?

• It shifts down

• It reflects over the x-axis

• It reflects over the y-axis

• It shifts up

How would you reflect the function f(x) = x^3 - 2x^2 - 2x over the y-axis?

• Place a negative sign in front of the function

• Replace x with -x

• No transformation needed

• Replace x with -x and place a negative sign in front

What is the effect of applying a negative sign to the entire expression of a polynomial function?

• It shifts the graph up

• It shifts the graph down

• It reflects the graph over the x-axis

• It reflects the graph over the y-axis

How can you reflect a function over both the x and y axes?

• No transformation needed

• Place a negative sign in front of the function

• Replace x with -x

• Replace x with -x and place a negative sign in front

What is the simplified way to write the reflection of a function over both axes?

• -f(x)

• f(-x)

• -f(-x)

• f(x)