Video Transcript
Which of the following relations
represents a function given that 𝑥 is the input and 𝑦 is the output?
To answer this question, we will
use the vertical line test. This is a graphical way of working
out whether a graph represents a function. If a graph represents a function,
any vertical line will intersect the function at most once. We will therefore add a vertical
line to our diagrams and inspect the number of points of intersection with the
curves. In figure (A), we observe that if
we add the vertical line 𝑥 equals five, the line intersects the curve twice. This means that graph (A) cannot
represent a function. The vertical line 𝑥 equals
negative four intersects the curve of graph (B) exactly once. We can translate this vertical line
by any distance horizontally, and this will always be the case. We can therefore conclude that
graph (B) represents a function. The correct answer is (B).
