B | math4u.vsb.cz

2000021006

Level:

Which of the following functions is an even function?

f (x) = | 1 - x | + | x + 1 |

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

h (x) = | 1 + x | + | x + 1 |

k (x) = | 1 - x | + | x - 1 |

2000021005

Level:

Which of the given statements about the domain

D (f)

of the function

f (x) = 3 | x + 2 | - | x - 1 |

is true?

D (f) = R

D (f) = [- 3; \infty)

D (f) = [- 2; 1]

D (f) = R ∖ {- 2; 1}

2000021004

Level:

Which of the given statements about the range

H (f)

of the function

f (x) = | 2 - x | + | 1 + x | - 2

is true?

H (f) = [1; \infty)

H (f) = R

H (f) = [- 1; 2]

H (f) = [- 1; \infty)

2000021003

Level:

Consider the function

f (x) = | x + 1 | - 2

. Which of the statements is true?

The function

f

has a minimum at the point

x = - 1

The function

f

has a minimum at the point

x = - 2

The function

f

has no minimum.

The function

f

has a maximum at the point

x = - 1

2000021002

Level:

In the picture, there is the graph of a function

f

. Specify its formula.

f (x) = | x + 1 | - 2 x; x \in [- 2; 3]

f (x) = | x + 1 | + 2 x; x \in [- 2; 3]

f (x) = | x - 1 | - 2 x; x \in [- 2; 3]

f (x) = | x - 1 | + 2 x; x \in [- 2; 3]

2000021001

Level:

In the picture, there is the graph of a function

f

. Which of the following statements is true?

The function

f

is bounded.

The function

f

has its maximum and has no minimum.

The function

f

is a one-to-one function and is decreasing.

The function

f

is an odd function and is bounded below.

2010013908

Level:

How many of the given functions have exactly one inflection point?

f (x) = \frac{1}{- 2 (x + 4)^{4}} + 6,

g (x) = - (x - 3)^{5} - (- 3 + x)^{3} + 1,

h (x) = \frac{x^{3} - 3 x^{2} + 6 x + 9}{- 3 x}

None of these functions has exactly one inflection point.

2010013907

Level:

How many of the given functions have exactly one inflection point?

f (x) = (x + 2)^{5} + (2 + x)^{3} - 2,

g (x) = \frac{1}{6 (x + 4)^{4}},

h (x) = \frac{x^{3} + 2 x^{2} + x + 2}{x}

None of these functions has exactly one inflection point.

2010013906

Level:

Suppose a function is convex up on the interval

[- 2; 1]

. Which one of the offered functions has that property?

h (x) = - \sqrt{x + 5}

f (x) = \frac{x - 2}{(x + 5)^{2}}

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

k (x) = - \frac{1}{5} x^{3} - 2 x^{2} + x + 1

2010013905

Level:

Suppose a function is concave down on the interval

[- 1; 2]

. Which one of the offered functions has that property?

g (x) = \sqrt{- 2 x + 8}

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

h (x) = \frac{x^{2} - 1}{x}

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

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