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9000007101

Level:

Consider a family

M

of quadratic functions, as shown in the picture. Any quadratic function in this family is given by the analytic expression

y = a x^{2} + b x + c

where

a

b

and

c

are real constants and

a \neq 0

. For each function the set

K

denotes the set of

x

-intercepts. Complete the statement. „The analytic expressions for functions in the family

M

differ only in ....”

the coefficient

a

the coefficient

b

the coefficient

c

the set

K

9000004905

Level:

In the following list identify a statement which is not true for the function

f : y = | \log (x - 3) - 1 |

The function

f

is increasing on the domain.

The domain of the function

f

(3; \infty)

All values of the function

f

are nonnegative.

The function

f

does not have a

y

-intercept.

The

x

-intercept of the function

f

x = 13

The function

f

is not one-to-one.

9000004901

Level:

Solve the following inequality.

\log_{0.3} x \geq \log_{0.3} 5

x \in (0; 5]

x \in (0; \infty)

x \in (- \infty; 5]

x \in [5; \infty)

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)

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})

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

9000007101

9000004905

9000004901

9000003809

9000002908

9000003607

9000003609

9000003709

9100004009

9100004010

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