Identifying Function Properties Using Algebra and Real-World Examples

The video tutorial explains how to determine if relations are functions using the vertical line test. It clarifies common misconceptions and provides examples, such as y = 3x + 1, which is a function, and y^2 = x + 1, which is not. The tutorial also covers 3y = 6x^2 - 6, showing it as a function. The video concludes with a review of these examples to solidify understanding.

What does the vertical line test determine about a graph?

• Whether the graph is a circle

• Whether each input has exactly one output

• Whether the graph is symmetrical

• Whether the graph is a straight line

Why is the relation y = 3x + 1 considered a function?

• Because it has two variables

• Because it passes the horizontal line test

• Because each input has exactly one output

• Because it is a quadratic equation

What is the main reason y^2 = x + 1 is not a function?

• It has only one variable

• It passes the vertical line test

• It is a linear equation

• It has more than one output for some inputs

How can you confirm that 3y = 6x^2 - 6 is a function?

• By checking if it passes the horizontal line test

• By isolating y and ensuring each input has one output

• By ensuring it has two variables

• By verifying it is a linear equation

What happens when you substitute a value for x in y = 3x + 1?

• The equation becomes undefined

• The equation becomes a quadratic

• You get exactly one output

• You get multiple outputs