Rational functions

9000007509

Level:

The graph of the function \[ f(x) = \frac{2x + 3} {2 - x} \] is a hyperbola. Find the center of this hyperbola.

$S = [2;-2]$

$S = [-2;2]$

$S = [2;2]$

$S ={\Bigl [ 2; \frac{3} {2}\Bigr ]}$

$S ={\Bigl [ 2;-\frac{3} {2}\Bigr ]}$

9000008006

Level:

Given the functions $f(x) = \frac{2} {x}$ and $g(x) = \frac{4} {x}$, identify a true statement.

$f(2) = g(4)$

$f\left (\frac{1} {2}\right ) = g(2)$

$f(1) > g(2)$

$f(4) < g(10)$

9000007510

Level:

The graph of the function \[ f(x) = \frac{-x + 1} {1 + 3x} \] is a hyperbola. Find the center of this hyperbola.

$S = \left [-\frac{1} {3};-\frac{1} {3}\right ]$

$S = \left [\frac{1} {3}; \frac{1} {3}\right ]$

$S = \left [1;-\frac{1} {3}\right ]$

$S = \left [-1;-\frac{1} {3}\right ]$

$S = \left [-\frac{1} {3}; \frac{1} {3}\right ]$

9000008007

Level:

Given the functions $f(x) = -\frac{3} {x}$ and $g(x) = 6$, solve $f(x) = g(x)$.

$-\frac{1} {2}$

$- 2$

$3$

$6$

9000008010

Level:

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.

$g(x) = \frac{3} {x}$

$g(x) = -\frac{3} {x}$

$g(x)= -\frac{1} {x}$

$g(x) = \frac{2} {x}$

9000008008

Level:

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 \[ g(2) = 2f(-2). \]

$4$

$2$

$- 1$

$- 2$

9000008005

Level:

Given the function $f(x)= -\frac{10} {x} $, evaluate $f(-5)\cdot f(2)$.

$- 10$

$2.5$

$1$

$2.5$

9000007601

Level:

Find the domain of the function $f(x) = 1 + \frac{3} {x+2}$.

$\mathbb{R}\setminus \{ - 2\}$

$\mathbb{R}\setminus \{2\}$

$\mathbb{R}\setminus \{1;2\}$

$\mathbb{R}\setminus \{ - 2;1\}$

$\mathbb{R}$

9000007501

Level:

The graph of the function \[ f(x) = 1 + \frac{3} {x + 2} \] is a hyperbola. Find the center of this hyperbola.

$S = [-2;1]$

$S = [3;1]$

$S = [1;3]$

$S = [1;-2]$

$S = [-2;3]$

9000008009

Level:

Given the function $f(x) = \frac{5} {x}$, find the function $g$ such that the graphs of $f$ and $g$ are symmetric about the line $y = x$.

$g(x) = \frac{5} {x}$

$g(x) = \frac{1} {x}$

$g(x)= -\frac{2} {x}$

$g(x) = -\frac{5} {x}$

9000007509

9000008006

9000007510

9000008007

9000008010

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9000008005

9000007601

9000007501

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