Function Properties and Transformations

The video tutorial explains how to determine if a function is even or odd using graphical and algebraic methods. Graphically, a function is even if it reflects over the y-axis and matches itself, and odd if it rotates 180 degrees around the origin and matches itself. Algebraically, substituting negative x into the function helps determine its nature: if the function remains unchanged, it's even; if it becomes the negative of the original, it's odd. The tutorial provides examples to illustrate these concepts and concludes with a summary of the methods discussed.

What is one graphical method to determine if a function is even?

• Reflect it over the x-axis

• Reflect it over the y-axis

• Rotate it 90 degrees

• Translate it vertically

How can you tell if a function is odd using its graph?

• Translate it horizontally

• Reflect it over the y-axis

• Reflect it over the x-axis

• Rotate it 180 degrees around the origin

What happens when you substitute -x into an even function?

• The function becomes undefined

• You get the negative of the original function

• You get the original function

• The function becomes zero

In the function f(x) = 2|x| - 4, what does substituting -x result in?

• 2|x| - 4

• 2|x| + 4

• -2|x| - 4

• -2|x| + 4

For the function f(x) = 2x^2 - 1, what does substituting -x result in?

• 2x^2 - 1

• -2x^2 + 1

• 2x^2 + 1

• -2x^2 - 1

What indicates that a function is neither even nor odd?

• The function equals its negative

• The function equals its original form

• The function does not match its original or negative form

• The function becomes zero

What is the result of substituting -x in a function with fractional exponents?

• The function becomes zero

• The function becomes undefined

• The function equals its original form

• The function equals its negative form

In the function f(x) = x^5 + x + 1, what does substituting -x result in?

• x^5 + x + 1

• -x^5 + x - 1

• -x^5 - x - 1

• x^5 - x + 1