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9000005808

Level:

Consider the linear functions

f (x) = x

g (x) = - x

and

h (x) = 3

. Consider also a triangle which is formed by the graphs of these three functions. Find the area of this triangle.

9

3

5

7

9000005807

Level:

Consider the function

f (x) = - x + 4

and a triangle which has one side on the graph of

f

and two other sides on the axes. Find the area of this triangle.

8

4

6

10

9000005809

Level:

Consider the functions

f (x) = x - 1

and

g (x) y = - x + a

. Find the value of the real parameter

a \in R

which ensure that the functions have a common value at

x = 3

, i.e.

f (3) = g (3)

a = 5

a = - 1

a = 1

a = 2

9000003607

Level:

The function

f (x) = {(\frac{1}{3})}^{x}

is graphed in the picture. Identify a possible analytic expression for the function

g

y = 3^{| x |} - 1

y = | {(\frac{1}{3})}^{x} - 1 |

y = {(\frac{1}{3})}^{| x |} - 1

y = {(\frac{1}{3})}^{| x - 1 |}

y = | 3^{x} - 1 |

y = 3^{| x - 1 |}

9000003609

Level:

Solve the following inequality.

{(\frac{3}{4})}^{x^{2} - 2 x} \leq \frac{4^{x - 6}}{3^{x - 6}}

x \in (- \infty; - 2] \cup [3; \infty)

x \in R ∖ {- 2; 3}

x \in R ∖ {- 3; 2}

x \in [- 2; 3]

9000003709

Level:

Solve the following inequality.

{(\frac{2}{3})}^{2 - 3 x} < \frac{2^{x + 1}}{3^{x + 1}}

(- \infty; \frac{1}{4})

(- \frac{1}{4}; \infty)

(- \infty; 4)

(\frac{1}{4}; \infty)

(4; \infty)

(- \infty; - \frac{1}{4})

9000003809

Level:

Find the solution set of the following inequality.

\log_{0.5} (x^{2} - 2 x) > \log_{0.5} 3

(- 1; 0) \cup (2; 3)

(- \infty; 0) \cup (2; \infty)

(0; 2)

(- \infty; - 1) \cup (0; 2) \cup (3; \infty)

(- \infty; - 1) \cup (3; \infty)

(- 1; 3)

9000002908

Level:

Find the intervals where the function

f (x) = | 1 + \frac{1}{x} |

is an increasing function. The function

f

is graphed in the picture.

[- 1; 0)

(- \infty; 1]

(- \infty; 0)

(0; \infty)

9100004009

Level:

Identify a possible graph of the function

g (x) = | | x - 2 | - 1 |

9100004010

Level:

Identify a possible graph of the function

g : y = | | x - 1 | - 1 | - 1

C

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