Exploring Rational Expressions in Algebra I

The video tutorial covers the concepts of functions and relations, explaining how each x-value in a function is paired with exactly one y-value. It discusses how to identify functions in tables by checking for unique x-values and explains the domain and range of functions, emphasizing that the domain includes all real numbers. The tutorial also introduces the vertical line test as a method to determine if a graph represents a function and demonstrates how to find the range from a graph by identifying which y-values are included.

What defines a function in terms of x and y values?

• Each x is paired with exactly one y.

• Each x is paired with multiple y values.

• No x values are paired with y values.

• Each y is paired with exactly one x.

If an x-value appears twice with different y-values, what does this imply?

• It is only a relation.

• It is not a function.

• It cannot be determined.

• It is still a function.

What does the vertical line test determine?

• The domain of the function.

• If a graph represents a relation.

• If a graph represents a function.

• The range of the function.

Which set of x-values indicates a function?

• All x-values are unique.

• x = -12 paired to y = 220, x = 0 paired to y = 2200.

• x-values are repeated with the same y-values.

• x = -8 paired to y = 220 and y = 21.

What is the domain of a function?

• Only positive x-values.

• All possible y-values.

• Only negative x-values.

• All possible x-values.

Can negative numbers be included in the domain of a function?

• Only if the function is linear.

• No, negative numbers are not allowed.

• Only if the function is non-linear.

• Yes, if the function allows it.

What does the range of a function represent?

• The minimum y-value.

• The maximum y-value.

• The set of all y-values.

• The set of all x-values.

Which y-value is NOT part of the range in the given function?

• y = 4

• y = 3

• y = 5

• y = 0

What does an open circle on a graph indicate about a y-value?

• The y-value is the minimum of the function.

• The y-value is not included in the range.

• The y-value is included in the range.

• The y-value is the maximum of the function.

Which graph passes the vertical line test and thus represents a function?

• Graph C

• Graph B

• Graph A

• Graph D