A | math4u.vsb.cz

2010012601

Level:

Find the area of the region bounded by the curves

y = e^{x} - 1

y = - e^{x} + 1

and

x = 1

2 e - 4

2 e - 2

2

4 - 2 e

2010012505

Level:

Identify a true statement about the function

f (x) = - \frac{3}{4} x^{4} + 2 x^{3}

The function

f

has a local maximum at

x = 2

The function

f

has a local minimum at

x = 0

The function

f

has two local extrema. These extrema are at

x = 0

and

x = 2

The function

f

has neither local minimum nor local maximum.

2010012406

Level:

Find the false statement about the function

f (x) = (x - 2)^{4} - 3

The function

f

is even.

The function

f

has the minimum at

x = 2

The function

f

is bounded below.

The range of the function

f

is the interval

[- 3; \infty)

2010012405

Level:

Find the true statement about the function

f (x) = (x + 1)^{3} - 2

The function

f

is an injective (one-to-one) function.

The function

f

is decreasing.

The function

f

is odd.

The function

f

has the minimum at

x = - 1

2010012404

Level:

In the following list identify a decreasing function.

f : y = - x^{3}

f : y = x^{4}

f : y = - x^{4}

f : y = x^{- 3}

f : y = - x^{2}

2010012403

Level:

Identify a function which is not one-to-one on the interval

[- 2; 2]

f : y = x^{2} - 2

f : y = x^{2} + 4 x

f : y = - x^{3}

f : y = (x - 2)^{2}

f : y = (x + 2)^{2}

f : y = x^{3} - 2

2010012402

Level:

Identify a function which is decreasing on

(- 3; 2)

f : y = (x - 2)^{2}

f : y = (x + 2)^{2}

f : y = (x + 3)^{2}

f : y = x^{2} - 2 x

f : y = - x^{2} + 1

f : y = x^{3}

2010012401

Level:

Identify a function which is increasing on

(- 1; \infty)

f : y = x^{3}

f : y = x^{4}

f : y = - x^{3}

f : y = x^{- 4}

f : y = - x^{- 2}

f : y = - x^{- 3}

2010012304

Level:

Let

f (x) = - x^{2}

. Given the graph of the function

f

and the graph of a function

g

which was obtained as a vertical shift of the graph of

f

(see the picture), choose the function

g

g (x) = - x^{2} + 2

g (x) = (x - 2)^{2}

g (x) = - x^{2} - 2

g (x) = (x + 2)^{2}

2010012303

Level:

Find the

y

-intercept of the following function.

f (x) = 6 x^{2} + 12 x - 7.2

[0; - 7.2]

[- 7.2; 0]

[6; 0]

There is no

y

-intercept.

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