1003101103
Level:
C
Find the true statement about the function \( f(x)=\log_2|x| \).
The function \( f \) is even.
The function \( f \) has the minimum at \( x=0 \).
The function \( f \) is bounded.
The function \( f \) is increasing.
Logarithmic functions
1003100001
Level:
A
In which of the following options is not given a logarithmic function?
\( f(x) = \log_{-2}x\)
\( g(x) = \log_{2}x\)
\( h(x) = \log_{\frac12}x\)
\( m(x) = \log_{0.2}x\)
1103099702
Level:
A
One of the given graphs is not the graph of a logarithmic function. Choose this graph.
1103099701
Level:
A
One of the given graphs is the graph of a logarithmic function. Choose this graph.
1103082705
Level:
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is false.
\( f(x)=\log_2|x|;\ x\in[0.25;8] \)
\( f(x)=|\log_2 x |;\ x\in[0.25;8] \)
\( f(x)=|-\log_2 x|;\ x\in[0.25;8] \)
\( f(x)=\left|\log_{\frac12} x \right|;\ x\in[0.25;8] \)
9000033705
Level:
C
Find the domain of the following function.
\[
f(x) = \sqrt{\log (x^{2 } + 2x + 1)}
\]
\(\left (-\infty ;-2] \cup [ 0;\infty \right )\)
\(\mathbb{R}\setminus \left \{-1\right \}\)
\(\left (-1;\infty \right )\)
\(\left (-\infty ;-1\right )\cup \left (1;\infty \right )\)
\(\left (-\infty ;0\right )\cup \left (2;\infty \right )\)
9000004810
Level:
B
In the following list identify a function which is not an increasing function.
\(y = 4x^{2}\)
\(y =\log _{4}x\)
\(y = 4x\)
\(y = 4^{x}\)
9000004903
Level:
A
Find the domain of the function \(f\colon y = \frac{3}
{\log _{5}(x-4)}\).
\(\mathrm{Dom}(f) = (4;5)\cup (5;\infty )\)
\(\mathrm{Dom}(f) = (0;\infty )\setminus \{4\}\)
\(\mathrm{Dom}(f) = (-4;\infty )\setminus \{5\}\)
\(\mathrm{Dom}(f) = (4;\infty )\)
9000004904
Level:
A
In the following list identify a function with a domain
\(\left (-\infty ; \frac{2}
{3}\right ).\)
\(y =\log (2 - 3x)\)
\(y =\log (3x - 2)\)
\(y = -\log (3x - 2)\)
\(y =\log (2x - 3)\)
\(y =\log (3 - 2x)\)
none of the above
9000004906
Level:
A
Identify a possible analytic expression for the function
\(f\)
graphed in the picture.
\(y =\log _{2}x\)
\(y =\log _{0.2}x\)
\(y =\log _{0.5}x\)
\(y =\log _{5}x\)