9000004909
Level:
A
Identify a possible analytic expression for the function
\(g\)
graphed in the picture.
\(y =\log _{3}(x + 2) - 1\)
\(y =\log _{\frac{1}
{3} }(x + 2) - 1\)
\(y =\log _{3}(x - 2) + 1\)
\(y =\log _{\frac{1}
{3} }(x - 2) + 1\)
Logarithmic Functions
9000004808
Level:
B
In the following list identify a function which is bounded below.
\(y = 3^{x}\)
\(y = -3^{x}\)
\(y =\log _{3}x\)
\(y = -\log _{3}x\)
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 \(f\colon y = \frac{3}
{\log _{5}(x-4)}\).
\(\mathrm{Dom}(f) = (4,5)\cup (5,\infty )\)
\(\mathrm{Dom}(f) = (0,\infty )\setminus \{4\}\)
\(\mathrm{Dom}(f) = (-4,\infty )\setminus \{5\}\)
\(\mathrm{Dom}(f) = (4,\infty )\)
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
9000003801
Level:
A
Identify a possible analytic expression for the function graphed in the picture.
\(y =\log _{\frac{1}
{2} }(x + 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) - 1\)
\(y =\log _{\frac{1}
{2} }(x + 1) - 1\)
9000003807
Level:
A
In the following list identify a negative expression.
\(\log _{0.1}20 -\log _{0.1}0.2\)
\(\log _{3}9^{2.5} -\log _{4}4^{0.5}\)
\(\log _{4}16^{\frac{3}
{2} } +\log _{3}3^{\frac{1}
{4} }\)
\(\log _{3}7 +\log _{3}\frac{81}
{7} \)
9000003802
Level:
A
In the following list identify a function with graph through the points
\([5,0]\) and
\([-1,-2]\).
\(y =\log _{2}(x + 3) - 3\)
\(y =\log _{5}(10 - x) - 1\)
\(y =\log _{3}(4 + x) - 2\)
\(y = 2 -\log _{3}(4 + x)\)
\(y = 3 -\log _{2}(x + 3)\)
\(y = 1 -\log _{5}(10 - x)\)
9000003803
Level:
B
The function \(g\colon y =\log _{3}(x - 2)\)
is graphed in the picture. In the following list identify a false statement.
The function \(g\)
is a positive function.
The domain of the function \(g\)
is the interval \((2,\infty )\).
The function \(g\)
is not bounded.
The function \(g\)
is an increasing function.
The function \(g\)
has neither minimum nor maximum.
The graph of the function \(g\)
goes through \([5,1]\).
9000003804
Level:
A
In the following list identify the point that is not a point on the graph of the function:
\[f(x) = 1 -\log _{3}x\]
\([0,1]\)
\([3,0]\)
\(\left [\frac{1}
{9},3\right ]_{}\)
\([1,1]\)
\(\left [\frac{1}
{3},2\right ]\)
\([9,-1]\)