The distance \(S\) an object travels under the influence of gravity in time \(t\) seconds is given by \(S(t) = \frac{1}{2} gt^2 + at + b\) where (\(g\)) is the acceleration due to gravity), \(a\), \(b\) are constants. Check if the function \(S(t)\) is one-to-one.
\(S(1) =\)
\(S(2) =\)
\(S(3) =\)
\(S(4) =\)
We can observe that,
Answer variants:
\(3a-b\)
\(4a+b\)
For every different values of \(t\), there will be same distance \(S\).
Hence, it is not a one-to-one function.
\(a+b\)
For every different values of \(t\), there will be different distance \(S\).
Hence, it is a one-to-one function.
\(4a-b\)
\(a+2b\)
\(2a-b\)
\(a+3b\)
\(3a+b\)
\(a-b\)
\(2a+b\)