Monotonic Functions and Tests

The video tutorial explains the concept of one-to-many relations and the vertical line test, which determines if a graph represents a function. It differentiates between relations and functions, using examples like circles and squares. The tutorial also introduces monotonic functions, explaining their characteristics and how they differ from other types of functions.

What does it mean when a single x-value corresponds to multiple y-values?

• It is a one-to-one function.

• It is a many-to-one function.

• It is a constant function.

• It is a one-to-many relation.

What is the purpose of the vertical line test?

• To determine if a graph is a circle.

• To calculate the area under a curve.

• To check if a graph represents a function.

• To find the slope of a line.

Why does a circle fail the vertical line test?

• Because it is not a closed shape.

• Because it has no x-values.

• Because a single x-value corresponds to multiple y-values.

• Because it is a straight line.

What is a relation in mathematical terms?

• A special type of function.

• A graph that passes the vertical line test.

• A line that is always increasing.

• A set of ordered pairs.

What is the relationship between squares and rectangles in terms of functions and relations?

• Every rectangle is a square.

• Rectangles are not functions.

• Every square is a rectangle.

• Squares and rectangles are unrelated.

How is a monotonic function defined?

• It is always increasing or always decreasing.

• It is a function with no x-values.

• It is a function that passes the horizontal line test.

• It changes direction frequently.

What happens to a function if it turns around at any point?

• It becomes a one-to-one function.

• It becomes a many-to-one relation.

• It remains a monotonic function.

• It becomes a constant function.

What is the significance of a function being monotonic?

• It fails the vertical line test.

• It is always a quadratic function.

• It never changes direction.

• It can be both increasing and decreasing.

Why is the horizontal line test not discussed in detail?

• It is not a mathematical concept.

• It is only used for circles.

• It is the same as the vertical line test.

• It is not relevant to identifying functions.

What does the horizontal line test determine?

• If a graph is a relation.

• If a function is one-to-one.

• If a graph is a circle.

• If a function is monotonic.