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9000009309

Level:

The speed of a swimmer in a

50 m

-pool is

0.8 m / s

. How fast will he swim two pool lengths (one pool length is

50

meters), if he/she needs

2 s

to turn at the end of the pool?

127 s

82 s

84 s

129 s

9000009310

Level:

The graph describes a distance traveled by a motorbike as a function of time. Find an analytic expression for this function.

s = 50 + 5 t, t \in [0; 30]

s = 5 + 50 t, t \in [0; 30]

s = 50 t, t \in [0; 30]

s = 5 t - 50, t \in [0; 30]

9000009311

Level:

The graph shows the speed of a train as a function of time. Find an analytic expression for this function.

v = 30 - \frac{3}{4} t, t \in [0; 20]

v = 30 + \frac{3}{4} t, t \in [0; 20]

v = 15 + \frac{3}{4} t, t \in [0; 20]

v = 30 - \frac{4}{3} t, t \in [0; 20]

9000009904

Level:

Consider the functions

f (x) = \frac{2}{x} and g (x) = \frac{2 x}{x^{2}} .

Is the conclusion

f = g

valid?

Yes.

No.

Yes, but only on

R^{+}

Yes, but only on

R^{-}

9000009906

Level:

Consider a function

f (x) = \frac{k}{x}

with a nonzero real parameter

k

. Describe what happens with the function

f

if the coefficient

k

changes the sign.

The function changes the type of monotonicity on the sets

R^{+}

and

R^{-}

(either from an increasing function into a decreasing function or vice versa).

The function changes its parity (from an odd function into an even function or from an even function into an odd function).

The domain of the function changes.

None of the above, both functions have the same parity, monotonicity and domain.

9000009907

Level:

Consider a function

f (x) = \frac{k}{x}

with a nonzero real parameter

k

. Suppose that the value of the coefficient

k

changes, but the sign of

k

remains the same. Describe which of the properties of

f

is changed.

None of the above, both functions have the same parity, monotonicity and range.

The function changes its parity (from an odd function into an even function or from en even function into an odd function).

The range of the function changes.

The function changes the type of monotonicity on the sets

R^{+}

and

R^{-}

(either from an increasing function into a decreasing function or vice versa).

9000009905

Level:

Consider the functions

f (x) = \frac{1}{2 x} and g (x) = \frac{k}{x} .

Identify the value of the coefficient

k

which ensures that the graphs of both functions are symmetric about

x

-axis.

- \frac{1}{2}

2

- 2

\frac{1}{2}

9000009901

Level:

The picture shows parts of the graphs of the functions

f (x) = \frac{k_{1}}{x} and g (x) = \frac{k_{2}}{x} .

Find the relationship between

k_{1}

and

k_{2}

k_{1} > k_{2}

k_{1} < k_{2}

k_{1} = k_{2}

No conclusion is possible, more of the above possibilities may occur.

9000010609

Level:

Identify a function which is a possible inverse to the function graphed in the picture.

y = x^{- 1}

x \in (0; \infty)

y = x

x \in (0; \infty)

y = - x

x \in (0; \infty)

y = - x^{- 1}

x \in (0; \infty)

y = x^{2}

x \in (0; \infty)

y = - x^{2}

x \in (0; \infty)

9000009909

Level:

Consider the system

\begin{aligned} y & = \frac{k}{x}, \\ y & = a, \end{aligned}

where

a

k

are real parameters and

x

y

are real variables. Determine the conditions for

a

and

k

so that the system has a unique solution in

R^{-} \times R^{-}

a < 0

and

k > 0

a < 0

and

k < 0

a > 0

and

k < 0

a > 0

and

k > 0

C

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