Understanding Functions in Graphs

The video tutorial explores whether y is a function of x in a given graph. It explains that for y to be a function of x, each x must map to exactly one y. The concept of a function machine is introduced, which should output a single value for each input. The graph is analyzed, revealing that the function is only defined at x = -2, where multiple y values are possible. This leads to the conclusion that y is not a function of x, as it does not map to a single output.

What is required for y to be considered a function of x?

• y must have exactly one value for each x

• y must have multiple values for each x

• x must have exactly one value for each y

• x must have multiple values for each y

In the function machine analogy, what should happen when an x is input?

• The machine should produce a random y value

• The machine should not produce any y value

• The machine should produce exactly one y value

• The machine should produce multiple y values

What does it mean if a function spits out multiple y values for a single x?

• The function is quadratic

• The function is linear

• The function is not well-defined

• The function is well-defined

What is the domain of the function in the given graph?

• x is equal to 2

• x is equal to 0

• x is equal to -2

• x is equal to 1

What happens when x = -2 is input into the function in the graph?

• It produces no y value

• It produces a negative y value

• It produces an infinite set of y values

• It produces a single y value

Which of the following points is on the relation when x = -2?

• (-2, -1)

• (-2, 0)

• (-2, 9)

• (-2, 5)

Why is y not a function of x in the given graph?

• Because y has a single value for each x

• Because y has multiple values for a single x

• Because x has multiple values for a single y

• Because x has a single value for each y

What conclusion can be drawn about the function in the graph?

• y is a function of x

• x is not a function of y

• y is not a function of x

• x is a function of y