Below is the graph of \(h=p(k)\).

The domain of \(p\) is \([-9, 8)\).

Define a new periodic function \(f(x)\) as follows

\[ f(x) = \begin{cases} p(x) & \text { if } x \in [-9, 8) \\ f(x \pm 17) & \text { otherwise } \end{cases} \]

Evaluate

\[ f(6) = \answer [tolerance=0.25]{-4} \]
\[ f(-6) = \answer [tolerance=0.25]{7} \]
\[ f(13) = \answer [tolerance=0.25]{1} \]
\[ f(170) = \answer [tolerance=0.25]{-1} \]
\[ f(-19) = \answer [tolerance=0.25]{0} \]
\[ f(-30) = \answer [tolerance=0.25]{0} \]

There exists a real number, \(M\), such that \(f(x)\) has no zeros for all \(x > M\).

True False

For any real number, \(r\), \(f\) has a zero in the interval \((r - 5, r + 5)\).

True False

For any \(\epsilon > 0\), the interval \((8 - \epsilon , 8 + \epsilon )\) contains a domain number, \(x_0\), such that \(f(x_0) > -4\).

True False
2025-05-17 23:05:56