2010011007
Level:
A
In the following list identify the point that is not a point on the graph of the function.
\[f(x)= -2\log _{2}x+3\]
\(\left[\frac12;1\right]\)
\([2;1]\)
\([4;-1]\)
\([1;3]\)
\(\left[\frac18;9\right]\)
\(\left[\frac14;7\right]\)
Logarithmic functions
2010011008
Level:
A
In the following list identify a positive expression.
\(\log _{0.5}3 -\log _{0.5}48\)
\(\log _{0.5}16 +\log _{0.5}4\)
\(\log _{3}9^3 -\log _{2}4^4\)
\(\log _{5}\left(4^{-1}\right) +\log _{5}\frac4{125}\)
2010016009
Level:
A
Given the function \(f(x)=\log_2(x^2+4)\), evaluate \(f(2)\cdot f(0)\).
\(6\)
\(32\)
\(0\)
\(24\)
2010016010
Level:
A
Given the function \(f(x)=\log_2(x+4)\), evaluate \(f(4)\cdot f(12)\).
\(12\)
\(48\)
\(128\)
\(4\)
9000003801
Level:
A
Identify a possible analytic expression for the function graphed in the picture.
\(y =\log _{\frac{1}
{2} }(x + 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) - 1\)
\(y =\log _{\frac{1}
{2} }(x + 1) - 1\)
9000003802
Level:
A
In the following list identify a function with graph through the points
\([5;0]\) and
\([-1;-2]\).
\(y =\log _{2}(x + 3) - 3\)
\(y =\log _{5}(10 - x) - 1\)
\(y =\log _{3}(4 + x) - 2\)
\(y = 2 -\log _{3}(4 + x)\)
\(y = 3 -\log _{2}(x + 3)\)
\(y = 1 -\log _{5}(10 - x)\)
9000003804
Level:
A
In the following list identify the point that is not a point on the graph of the function:
\[f(x) = 1 -\log _{3}x\]
\([0;1]\)
\([3;0]\)
\(\left [\frac{1}
{9};3\right ]_{}\)
\([1;1]\)
\(\left [\frac{1}
{3};2\right ]\)
\([9;-1]\)
9000003807
Level:
A
In the following list identify a negative expression.
\(\log _{0.1}20 -\log _{0.1}0.2\)
\(\log _{3}9^{2.5} -\log _{4}4^{0.5}\)
\(\log _{4}16^{\frac{3}
{2} } +\log _{3}3^{\frac{1}
{4} }\)
\(\log _{3}7 +\log _{3}\frac{81}
{7} \)
9000004902
Level:
A
Find the domain of the function \(f\colon y =\log _{\frac{1}
{3} }(9 - x^{2})\).
\(\mathrm{Dom}(f) = (-3;3)\)
\(\mathrm{Dom}(f) =\mathbb{R}\setminus \{3\}\)
\(\mathrm{Dom}(f) = (-\infty ;3)\)
\(\mathrm{Dom}(f) = (3;\infty )\)
\(\mathrm{Dom}(f) = (-\infty ;-3)\cup (3;\infty )\)
9000004903
Level:
A
Find the domain of the function \(f\colon y = \frac{3}
{\log _{5}(x-4)}\).
\(\mathrm{Dom}(f) = (4;5)\cup (5;\infty )\)
\(\mathrm{Dom}(f) = (0;\infty )\setminus \{4\}\)
\(\mathrm{Dom}(f) = (-4;\infty )\setminus \{5\}\)
\(\mathrm{Dom}(f) = (4;\infty )\)