9000004808
Level:
B
In the following list identify a function which is bounded below.
\(y = 3^{x}\)
\(y = -3^{x}\)
\(y =\log _{3}x\)
\(y = -\log _{3}x\)
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.
9000004902
Level:
A
Find the domain of the function \(f\colon y =\log _{\frac{1}
{3} }(9 - x^{2})\).
\(\mathrm{Dom}(f) = (-3;3)\)
\(\mathrm{Dom}(f) =\mathbb{R}\setminus \{3\}\)
\(\mathrm{Dom}(f) = (-\infty ;3)\)
\(\mathrm{Dom}(f) = (3;\infty )\)
\(\mathrm{Dom}(f) = (-\infty ;-3)\cup (3;\infty )\)
9000003802
Level:
A
In the following list identify a function with graph through the points
\([5;0]\) and
\([-1;-2]\).
\(y =\log _{2}(x + 3) - 3\)
\(y =\log _{5}(10 - x) - 1\)
\(y =\log _{3}(4 + x) - 2\)
\(y = 2 -\log _{3}(4 + x)\)
\(y = 3 -\log _{2}(x + 3)\)
\(y = 1 -\log _{5}(10 - x)\)
9000003801
Level:
A
Identify a possible analytic expression for the function graphed in the picture.
\(y =\log _{\frac{1}
{2} }(x + 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) + 1\)
\(y =\log _{\frac{1}
{2} }(x - 1) - 1\)
\(y =\log _{\frac{1}
{2} }(x + 1) - 1\)
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:
\[f(x) = 1 -\log _{3}x\]
\([0;1]\)
\([3;0]\)
\(\left [\frac{1}
{9};3\right ]_{}\)
\([1;1]\)
\(\left [\frac{1}
{3};2\right ]\)
\([9;-1]\)
9000003807
Level:
A
In the following list identify a negative expression.
\(\log _{0.1}20 -\log _{0.1}0.2\)
\(\log _{3}9^{2.5} -\log _{4}4^{0.5}\)
\(\log _{4}16^{\frac{3}
{2} } +\log _{3}3^{\frac{1}
{4} }\)
\(\log _{3}7 +\log _{3}\frac{81}
{7} \)
9100004907
Level:
A
Identify a possible graph of the function
\(f\colon y =\log _{0.2}x\).
