In a correspondence diagram, which visual clue indicates that the underlying relation fails to be a function?

Let $f$ be the one-to-one function defined by ordered pairs $\left\{(-3,0),(-1,2),(2,5),(4,7)\right\}$. Which ordered pairs define $f^{-1}$?

Given the continuous curve $y=\sin \left(x\right)$ restricted to domain $[-\frac{\pi }{2},\frac{\pi }{2}]$ and codomain $[-1,1]$, evaluate whether the restricted function has an inverse on the codomain, and if so, what is an explicit form for that inverse.

Solve $2^{x+1}=2^3$ for $x$.

An exponential function $f\left(x\right)=b^x$ passes through the points $(0,1)$, $(1,8)$, and $(2,64)$. What is the value of $b$?

Approximate the value of ${1.0001}^{10000}$. Round the final answer to four decimal places.

What is the exact value of ${\log }_2\left(16\right)$?

Solve $3^{2x-1}=81$ for $x$.

Simplify ${\log }_{{}_{16}}\left(8\right)$.

True or False: The statement ${\log }_{10}\left(1000\right)=3$ means ${10}^3=1000$.

Use the power property to rewrite $3{\log }_{4}2$.

Condense into a single logarithm: $4{\log }_5\left(x\right)-{\log }_5(x+2)$