When you graph a function or relation, the input is given by the horizontal axis
and the output is given by the vertical axis.
SUMMARY
Vertical Line Test for Functions
Student Help
A graph is a function if no vertical line intersects the graph at more
than one point.
STUDY TIP
You can use your
pencil to check. Keep
your pencil straight to
represent a vertical
line and pass it across
the graph. If it touches
the graph at more than
one point, the graph is
not a function.
y
y
function
2
EXAMPLE
x
x
not a function
not a function
x
x
y
y
function
Use the Vertical Line Test
Use the vertical line test to determine whether the graph represents a function.
a.
b.
y
y
x
x
Solution
a. No vertical line can intersect the
graph more than once. So, this graph
does represent y as a function of x.
y
b. It is possible to draw a vertical line
x
that intersects the graph twice. So,
this graph does not represent a
function.
Use the Vertical Line Test
Use the vertical line test to determine whether the graph represents
a function.
1.
2.
y
y
x
x
4.8
Functions and Relations
253