9000008006
Level:
A
Given the functions \(f(x) = \frac{2}
{x}\)
and \(g(x) = \frac{4}
{x}\),
identify a true statement.
\(f(2) = g(4)\)
\(f\left (\frac{1}
{2}\right ) = g(2)\)
\(f(1) > g(2)\)
\(f(4) < g(10)\)
Rational Functions
9000007601
Level:
B
Find the domain of the function \(f(x) = 1 + \frac{3}
{x+2}\).
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{1,2\}\)
\(\mathbb{R}\setminus \{ - 2,1\}\)
\(\mathbb{R}\)
9000008007
Level:
A
Given the functions \(f(x) = -\frac{3}
{x}\)
and \(g(x) = 6\),
solve \(f(x) = g(x)\).
\(-\frac{1}
{2}\)
\(- 2\)
\(3\)
\(6\)
9000007602
Level:
B
Find the domain of the function \(f(x) = 2 - \frac{3}
{x-2}\).
\(\mathbb{R}\setminus \{2\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2,2\}\)
\(\mathbb{R}\setminus \{ - 3\}\)
\(\mathbb{R}\)
9000008008
Level:
C
Given the functions
\[
\text{$f(x) = -\frac{2}
{x}$ and $g(x)= \frac{k}
{x}$}
\]
find the value of the parameter \(k\in \mathbb{R}\setminus \{0\}\)
which ensures
\[
g(2) = 2f(-2).
\]
\(4\)
\(2\)
\(- 1\)
\(- 2\)
9000007604
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{|x|+1}\right |\).
\(\mathbb{R}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\setminus \{ - 1,0,1\}\)
\(\mathbb{R}\setminus \{1\}\)
9000008010
Level:
A
Given the function
\(f\colon y = -\frac{3}
{x}\).
find the function \(g\) such
that the
graphs of \(f\)
and \(g\) are
symmetric
about the \(x\)-axis.
\(g(x) = \frac{3}
{x}\)
\(g(x) = -\frac{3}
{x}\)
\(g(x)= -\frac{1}
{x}\)
\(g(x) = \frac{2}
{x}\)
9000007605
Level:
C
Find the domain of the function \(f(x) = 1 + \left | \frac{1}
{-|x|+1}\right |\).
\(\mathbb{R}\setminus \{ - 1,1\}\)
\(\mathbb{R}\setminus \{ - 1\}\)
\(\mathbb{R}\setminus \{ - 1,0,1\}\)
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\)
9000008005
Level:
A
Given the function \(f(x)= -\frac{10}
{x} \),
evaluate \(f(-5)\cdot f(2)\).
\(- 10\)
\(2.5\)
\(1\)
\(2.5\)
9000007606
Level:
B
Find the range of the function \(f(x) = 1 + \frac{3}
{x+2}\).
\(\mathbb{R}\setminus \{1\}\)
\(\mathbb{R}\setminus \{ - 2\}\)
\(\mathbb{R}\setminus \{ - 2,1\}\)
\([ 0,\infty )\)
\(\mathbb{R}\)