Two things to check here:

·
In the area of the graph to the *right* of the y-axis, does
one variable increase as the other variable decreases? The area of the graph
to the *left* of the y-axis is a bit tricky – for _{}, as x decreases (goes
more negative), y gets larger (becomes less negative). However, for _{}, as x decreases,
y decreases too.

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·
Is the graph *undefined* at x = 0 (where the y-axis usually
is)? This should happen regardless of what type of inverse relationship it is,
because there’s a divide by ‘x’ or divide by ‘x^{2}’ or something
similar. Since x is zero, dividing by ‘0’ gets you an undefined number. The
value of ‘y’ near x = 0 should be either a very large positive number or a very
large negative number.

Here’s a heap of graphs that *aren’t* inverse
relationships:

Not inverse relationships |

These graphs are inverse relationships:

This graph doesn’t pass through the origin, which is
OK. To the right of the y-axis, as x increases, y decreases, which is OK. To
the left of the x-axis as x decreases, y increases. It also appears that the
value of y gets very large and positive as you approach x = 0 from the right
side of the y-axis. It also seems to get very large and negative when you
approach from the left side of the y-axis. Because the graph is mirror imaged
both across the x-axis *and *y-axis, it’s probably of the form _{}, or _{}, or _{} – the power of x
in the denominator will be an *odd* number.

This graph doesn’t pass through the origin which is
OK. To the right of the y-axis, as x increases y decreases, which is OK. To
the left of the y-axis, as x decreases, y decreases too. This is OK as well –
it just means that the inverse relationship is going to be like _{}, _{} – the power of
‘x’ in the denominator will be an *even* number (remember that a negative
x raised to an even power will give a positive answer, which makes sense since
all the values of y to the left of the y-axis are positive).