Below is the graph of \(y=f(t)\).

What is the domain of \(f\)?

\[ \left [ \answer [tolerance=0.25]{-4}, \answer [tolerance=0.25]{6} \right ] \]

Evaluate \(f(-4) = \answer [tolerance=0.25]{-1}\)

Classify \(4\).

Discontinuity Singularity Neither

\(-1\) is a local maximum of \(f\) occuring at \(-4\).

True False

Evaluate \(f(6) = \answer [tolerance=0.25]{2}\)

Classify \(6\).

Discontinuity Singularity Neither

\(2\) is a local minimum of \(f\) occuring at \(6\).

True False

\(g\) is increasing on \((-4, 6)\).

True False

\(g\) is increasing on \([-4, 6]\).

True False

\(g\) is increasing on \([-4, 6)\).

True False

\(g\) is increasing on \((-4, 6]\).

True False

There exists a real number, \(M\), such that \(f(t) < M\) for all \(t\).

True False

\(f\) has a global maximum.

True False

There exists a real number, \(M\), such that \(f(t) > M\) for all \(t\).

True False

\(f\) has a global minimum.

True False

For every \(\epsilon > 0\), the interval \((-4-\epsilon , -4+\epsilon )\) contains a domain number.

True False

For every \(\epsilon > 0\), the interval \((-4-\epsilon , -4+\epsilon )\) contains a domain number, \(d\), such that \(f(d) - f(-4) > 1\).

True False

For every \(\epsilon > 0\), the interval \((6-\epsilon , 6+\epsilon )\) contains a domain number.

True False

For every \(\epsilon > 0\), the interval \((6-\epsilon , 6+\epsilon )\) contains a domain number, \(d\), such that \(f(d) - f(6) > 1\).

True False
2025-05-17 23:04:33