Exploring Even and Odd Functions and Their Symmetries

The video tutorial by Math Camp 321 explains the concepts of even and odd functions, focusing on their symmetry properties. Even functions exhibit symmetry over the y-axis, while odd functions have symmetry over the origin. The tutorial provides examples of each type, including absolute value, quadratic, cosine, and reciprocal functions for even functions, and identity, cubic, sine, and reciprocal functions for odd functions. The video also offers tips on identifying these functions without a graph.

What does the term 'even' or 'odd' refer to in functions?

• The range of the function

• The symmetry of the function

• The degree of the function

• The domain of the function

Which of the following functions is an example of an even function?

• y = 1/x

• y = x

• y = x^3

• y = |x|

What characteristic does a function with y-axis symmetry exhibit?

• It is an odd function

• It is a periodic function

• It is a linear function

• It is an even function

Which function is described as looking like a 'V' and is shifted down one unit?

• y = |x| - 1

• y = x^2

• y = 1/x^2

• y = cos(x)

What is the shape of the graph of y = x^2 + 2?

• A straight line

• A parabola

• A hyperbola

• A sine wave

Which trigonometric function is an example of an even function?

• tan(x)

• cos(x)

• cot(x)

• sin(x)

What type of symmetry does an odd function exhibit?

• No symmetry

• Symmetry over the y-axis

• Symmetry over the x-axis

• Symmetry over the origin

Which function is known as the 'identity function' and is an example of an odd function?

• y = x

• y = x^2

• y = |x|

• y = 1/x

What is the shape of the graph of y = x^3?

• A straight line

• A sine wave

• A parabola

• A wiggle

Which function looks like two boomerangs in opposing quadrants and is an odd function?

• y = 1/x

• y = x^2

• y = |x|

• y = cos(x)