A | math4u.vsb.cz

9000081405

Level:

Find the inequality which describes the set graphed in the picture.

$|2 - x| < 1;\ x\in \mathbb{R}$

$|2 + x| > 1;\ x\in \mathbb{R}$

$|2 + x| < 1;\ x\in \mathbb{R}$

$|2 - x| > 1;\ x\in \mathbb{R}$

$|1 - x| < 2;\ x\in \mathbb{R}$

9000083701

Level:

Find all the values of $x\in \mathbb{R}$ for which the given expression equals zero. \[ \frac{x^{2} - 16} {2x - 8} \]

$x = -4$

$x = 4$

$x =\pm 4$

$x = 0$

9000079210

Level:

Consider the expression \[ V (x) = \frac{x} {x - 1} - \frac{1} {1 - x}. \] Find the correct ordering of the values $V (-2)$, $V (0)$ and $V (2)$.

$V (0) < V (-2) < V (2)$

$V (-2) < V (0) < V (2)$

$V (0) < V (2) < V (-2)$

$V (2) < V (0) < V (-2)$

9000079206

Level:

Assuming $x\neq 0$, $y\neq 0$, $x\neq y$, simplify the following expression. \[ { \frac{1} {x^{2}} - \frac{1} {y^{2}} \over -\frac{1} {y} + \frac{1} {x}} \]

$\frac{x+y} {xy} $

$-\frac{x+y} {xy} $

$\frac{1} {y} -\frac{1} {x}$

$\frac{1} {x} -\frac{1} {y}$

9000078509

Level:

Evaluate the following expression. \[ |3 - 7|-|2(-4)| + |(-5)(-2)| \]

$6$

$14$

$22$

$- 2$

9000079101

Level:

Find the intervals of monotonicity for the following function. \[ f(x)= \frac{3x + 1} {2x - 5} \]

Decreasing on $\left (-\infty ; \frac{5} {2}\right )$ and $\left (\frac{5} {2};\infty \right )$.

Decreasing on $\left (-\infty ; \frac{5} {2}\right )\cup \left (\frac{5} {2};\infty \right )$.

Decreasing on $\left (-\infty ; \frac{5} {2}\right )$, increasing on $\left (\frac{5} {2};\infty \right )$.

Increasing on $\left (-\infty ; \frac{5} {2}\right )$, decreasing on $\left (\frac{5} {2};\infty \right )$.

9000079102

Level:

Find the intervals where the following function is a decreasing function. \[ f(x) = \frac{x^{2} + 1} {x} \]

$[ - 1;0)$ and $(0;1] $

$[ - 1;1] $

$(-\infty ;-1] $ and $[1;\infty) $

$[1;\infty) $

9000079103

Level:

Find the $x$ at which has the function $f$ a local maximum. \[ f(x) = x^{3} - 3x^{2} - 9x + 2 \]

$x=- 1$

$x=- 3$

$x=1$

$x=3$

9000079104

Level:

Find the $x$ at which has the function $f$ a local minimum. \[ f(x) = \frac{\ln x} {x} \]

does not exist

$x = 0$

$x = 1$

$x =\mathrm{e}$

9000079105

Level:

Find all the $x$ at which the function $f$ has local extrema. \[ f(x)= \left (1 - x^{2}\right )^{3} \]

$x=0$

$x_1=0$, $x_2=1$

$x_1=- 1$, $x_2=1$

$x_1=- 1$, $x_2=0$, $x_3=1$

A

9000081405

9000083701

9000079210

9000079206

9000078509

9000079101

9000079102

9000079103

9000079104

9000079105

About portal

O portálu