Analyzing function behavior

9000142004

Level:

Identify a correct statement related to the function $f$ shown in the picture.

concave up on $(-\infty ;1)$, concave down on $(1;\infty )$, no inflection

concave up on $(-\infty ;1)$, concave down on $(1;\infty )$, inflection at $x = 1$

concave up on $(1;\infty )$, concave down on $(-\infty ;1)$, inflection at $x = 1$

concave up on $(1;\infty )$, concave down on $(-\infty ;1)$, no inflection

9000142005

Level:

Identify a correct statement related to the function $f$ shown in the picture.

concave up on $(-1;0)$ and $(1;\infty )$, concave down on $(-\infty ;-1)$ and $(0;1)$, inflection at $x_{1} = -1$, $x_{2} = 0$ and $x_{3} = 1$

concave up on $(-1;0)\cup (1;\infty )$, concave down on $(-\infty ;-1)\cup (0;1)$, inflection at $x_{1} = -1$, $x_{2} = 0$ and $x_{3} = 1$

concave up on $(-\infty ;-1)$ and $(0;1)$, concave down on $(-1;0)$ and $(1;\infty )$, inflection at $x_{1} = -1$, $x_{2} = 0$ and $x_{3} = 1$

concave up on $(-\infty ;-1)\cup (0;1)$, concave down on $(-1;0)\cup (1;\infty )$, inflection at $x_{1} = -1$, $x_{2} = 0$ and $x_{3} = 1$

9000142006

Level:

Identify a correct statement related to the function $f$ shown in the picture.

concave up on $(-\infty ;0)$ and $(1;\infty )$, concave down on $(0;1)$, a unique inflection at $x = 0$

concave up on $(-\infty ;0)$ and $(1;\infty )$, concave down on $(0;1)$, inflection at $x_{1} = 0$ and $x_{2} = 1$

concave up on $(-\infty ;0)\cup (1;\infty )$, concave down on $(0;1)$, a unique inflection at $x = 0$

concave up on $(0;1)$, concave down on $(-\infty ;0)$ and $(1;\infty )$, inflection at $x_{1} = 0$ and $x_{2} = 1$

1003259601

Level:

Find all the asymptotes of the graph of the function $ f(x)=2x+\frac2{x-3} $.

$ x=3 $, $ y=2x $

$ y=3 $, $ y=2x $

$ x=3 $, $ y=-2x $

$ x=2 $, $ y=3x $

$ x=3 $, $ y=2 $

1003259602

Level:

Find all the asymptotes of the graph of the function $ f(x)=x+\frac{2x}{x^2-1} $.

$ x=-1 $, $ x=1 $, $ y=x $

$ x=-1 $, $ x=1 $, $ y=1 $

$ x=-1 $, $ x=1 $, $ y=x+1 $

$ x=-1 $, $ x=1 $

$ x=-1 $, $ x=1 $, $ y=0 $

1003259603

Level:

Find all the asymptotes of the graph of the function $ f(x)=\frac{x}{x^2+1} $.

$ y=0 $

there is no an asymptote

$ x=0 $

$ x=-1 $, $ y=0 $

1003259604

Level:

Find all the asymptotes of the graph of the function $ f(x)=\frac1{1-x^2} $.

$ x=1 $, $ x=-1 $, $ y=0 $

$ x=1 $, $ x=-1 $

$ x=1 $, $ x=-1 $, $ y=1 $

$ y=1 $, $ y=-1 $, $ y=0 $

$ x=1 $, $ y=0 $

1003259605

Level:

Find all the asymptotes of the graph of the function $ f(x)=\frac1{x-2}+x-1 $.

$ x=2 $, $ y=x-1 $

$ x=2 $, $ y=x $

$ x=2 $

$ x=2 $, $ y=1 $

$ x=2 $, $ y=-1 $

1003259606

Level:

Find all the asymptotes of the graph of the function $ f(x)=\mathrm{e}^{\frac1x} $.

$ x=0 $, $ y=1 $

$ x=0 $, $ y=0 $

$ x=0 $

there is no an asymptote

$ x=0 $, $ y=-1 $

1003259607

Level:

Find all the asymptotes of the graph of the function $ f(x)=x\mathrm{e}^{\frac1x} $.

$ x=0 $, $ y=x+1 $

$ x=0 $, $ y=x-1 $

$ x=0 $

there is no an asymptote

$ x=0 $, $ y=1 $

Analyzing function behavior

9000142004

9000142005

9000142006

1003259601

1003259602

1003259603

1003259604

1003259605

1003259606

1003259607

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