Functions and Their Properties

The video tutorial introduces the concept of functions, explaining their notation and how they relate to inputs and outputs. It explores the equations of parabolas and differentiates between relations and functions. The tutorial also analyzes circles to illustrate when a relation is not a function and introduces the vertical line test as a method to determine if a graph represents a function.

What are the classic labels used for inputs and outputs in functions?

• m and n

• a and b

• x and y

• p and q

What does it mean when we say y is a function of x?

• Y depends on x

• Y and x are unrelated

• Y is independent of x

• X depends on y

If a parabola has roots at -1 and 2, what is one possible factorization?

• (x - 1)(x + 2)

• (x + 1)(x - 2)

• (x + 1)(x + 2)

• (x - 1)(x - 2)

What is the output when x = 0 for the function (x + 1)(x - 2)?

• 2

• 0

• -2

• 1

What is the equation of the unit circle?

• x^2 + y^2 = 0

• x^2 + y^2 = 1

• x^2 - y^2 = 0

• x^2 - y^2 = 1

Why is the unit circle not considered a function?

• It has multiple outputs for a single input

• It has only one output for each input

• It has no outputs

• It has no inputs

Which x values on the unit circle provide only one y output?

• x = 0

• x = 2

• x = 1 and x = -1

• x = -2

What is the vertical line test used for?

• To determine if a graph is a function

• To determine if a graph is a line

• To determine if a graph is a circle

• To determine if a graph is a parabola

What happens if a vertical line intersects a graph at more than one point?

• The graph is a function

• The graph is not a function

• The graph is a line

• The graph is a parabola

What is the conclusion if a vertical line intersects a graph at only one point everywhere?

• The graph is a parabola

• The graph is a function

• The graph is not a function

• The graph is a circle