Functions and the Vertical Line Test (3.6.1)

Question 1

• A relation is a set of ordered pairs in which any given x-value may be paired with more than one y-value.

Answer 1

• A relation is a set of ordered pairs in which any given x-value may be paired with more than one y-value.

Question 2

• A function is a set of ordered pairs in which each x-value is matched with exactly one y-value.

Answer 2

• A function is a set of ordered pairs in which each x-value is matched with exactly one y-value.

Question 3

If each time you use a specific value for x in an equation, you
get exactly one value for y, then the equation is a function.
In this example, solving for a random value, x = 1, you get
exactly one answer, y = 36. Only one y-value is possible for
this or any other x, so the equation qualifies as a function.
In this example, if you solve for x = 2, you get exactly one
answer, y = 49. Only one y-value is possible for this or any
other x, so the equation qualifies as a function.
In this example, if you solve for x = $5, you get exactly one
answer, y = $100. Only one y-value is possible for this or
any other x, so the equation qualifies as a function.
The graph on the left represents a function. No matter where
you place the vertical line it passes through only one point
on the curve. For each x there is only one (x,y) point.
The graph on the right does not represent a function because
the vertical line passes through more than one point. This
type of graph represents a relation

Answer 3

If each time you use a specific value for x in an equation, you
get exactly one value for y, then the equation is a function.
In this example, solving for a random value, x = 1, you get
exactly one answer, y = 36. Only one y-value is possible for
this or any other x, so the equation qualifies as a function.
In this example, if you solve for x = 2, you get exactly one
answer, y = 49. Only one y-value is possible for this or any
other x, so the equation qualifies as a function.
In this example, if you solve for x = $5, you get exactly one
answer, y = $100. Only one y-value is possible for this or
any other x, so the equation qualifies as a function.
The graph on the left represents a function. No matter where
you place the vertical line it passes through only one point
on the curve. For each x there is only one (x,y) point.
The graph on the right does not represent a function because
the vertical line passes through more than one point. This
type of graph represents a relation