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

What is the domain of \(f\)?

\([-5, 0) \cup (0, 4)\) \([-5, 4)\) \((-\infty , \infty )\) \((-\infty , 0) \cup (0, \infty )\) \([-8, -3] \cup (1, 9)\)

Evaluate \(f(0) = \answer [tolerance=0.25]{-3}\)

Classify \(0\).

Discontinuity Singularity Neither

\(f\) is increasing on \((-5, 0)\).

True False

\(f\) is increasing on \([-5, 0]\).

True False

\(f\) is increasing on \((-5, 0]\).

True False

\(f\) is increasing on \([-5, 0)\).

True False

\(f\) is increasing on \((0, 4)\).

True False

\(f\) is increasing on \([0, 4]\).

True False

\(f\) is increasing on \([0, 4)\).

True False

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

True False

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

True False

For any \(\epsilon > 0\), there exists a domain number in the interval \((0-\epsilon , 0+\epsilon )\).

True False

For any \(\epsilon > 0\), there exists a domain number in the interval \((-5-\epsilon , -5+\epsilon )\).

True False

For any \(\epsilon > 0\), there exists a domain number, \(d\), in the interval \((0-\epsilon , 0+\epsilon )\) such that \(f(d) - f(0) > 1\).

True False

There exists an open interval, \(I\), such that \(2 < f(c) < 6\) for all \(c \in I\).

True False

There exists a domain number, \(c\), such that \(f(c) < -9\).

True False

How many zeros does \(f\) have?

\(0\) \(1\) \(2\) \(3\) \(4\)

\(f\) is an increasing function.

True False

\(f\) is continuous on the interval \((1, 3)\).

True False
2025-05-17 23:01:33