Symmetry and Characteristics of Functions

The video introduces a new notation for functions, explaining how it differs from traditional algebraic interpretations. It explores graph symmetry, using examples like y = x and y = x^2, and discusses different types of symmetry, including reflectional and rotational. The video concludes with an explanation of even and odd functions, highlighting their unique properties and symmetries.

What does the notation f(x) represent in the context of functions?

• A constant value

• The sum of f and x

• A function named f with input x

• The product of f and x

Which of the following is an example of a graph with symmetry?

• y = x + 1

• y = x^2

• y = 2x

• y = x^3

How would you describe the symmetry of the graph y = x?

• Symmetrical about y = x

• Symmetrical about x = 0

• Symmetrical about y = -x

• Symmetrical about y = 0

What is the primary difference between y = x^3 and y = tan(x) at the origin?

• y = tan(x) pauses at the origin

• y = tan(x) has a horizontal tangent

• y = x^3 has a horizontal tangent

• y = x^3 passes through the origin at a 45-degree angle

What type of symmetry does y = x^3 exhibit?

• Reflectional symmetry

• Rotational symmetry

• No symmetry

• Symmetrical about y = x

What is the defining characteristic of an even function?

• It has no symmetry

• It is symmetrical about the x-axis

• It is symmetrical about the origin

• It is symmetrical about the y-axis

Which of the following functions is considered an odd function?

• y = x^6

• y = x^2

• y = x^3

• y = x^4

Why do higher power even functions like x^4 have the same symmetry as x^2?

• They have no symmetry

• They are symmetrical about the origin

• They are symmetrical about the y-axis

• They are symmetrical about the x-axis

What happens to the graph of y = x^4 compared to y = x^2?

• It remains the same

• It becomes narrower

• It becomes wider

• It shifts upwards

What is the symmetry of y = x^3 called?

• No symmetry

• Odd symmetry

• Reflectional symmetry

• Even symmetry