Answer
a) NOT a one-to-one function
b) a one-to-one function
Work Step by Step
a) Some of the ordered pairs of the given function, $
f(x)=x^2+9
$, are $
\left\{(-2,13)(-1,10),(0,9),(1,10),(2,13),...\right\}
$. Note that the $y$-coordinates are NOT unique (i.e $13$ is paired with both $-2$ and $2$). Hence, the given function is NOT a one-to-one function.
b) Any horizontal line drawn on the given graph of the function will intersect it in at most $1$ point. Hence, the given graph is a one-to-one function.
