Logarithmic Functions

9000004905

Level: 
C
In the following list identify a statement which is not true for the function \(f\colon y = |\log (x - 3) - 1|\).
The function \(f\) is increasing on the domain.
The domain of the function \(f\) is \((3,\infty )\).
All values of the function \(f\) are nonnegative.
The function \(f\) does not have a \(y\)-intercept.
The \(x\)-intercept of the function \(f\) is \(x = 13\).
The function \(f\) is not one-to-one.

9000033705

Level: 
C
Find the domain of the following function. \[ f(x) = \sqrt{\log (x^{2 } + 2x + 1)} \]
\(\left (-\infty ,-2] \cup [ 0,\infty \right )\)
\(\mathbb{R}\setminus \left \{-1\right \}\)
\(\left (-1,\infty \right )\)
\(\left (-\infty ,-1\right )\cup \left (1,\infty \right )\)
\(\left (-\infty ,0\right )\cup \left (2,\infty \right )\)