Rational functions

1003118306

Level:

Find the true statement about the function

f (x) = | \frac{4 x - 4}{2 x - 1} |

The domain of the function

f

is the set

(- \infty; \frac{1}{2}) \cup (\frac{1}{2}; \infty)

The range of the function

f

is the set

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

The function

f

has the minimum at

x = 4

The function

f

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

1003118307

Level:

Identify which of the following functions has the maximum at

x = - \frac{1}{2}

m (x) = - | \frac{4 x + 2}{x - 2} |

g (x) = | - \frac{5 x + 10}{2 x - 1} |

f (x) = - | \frac{2 x + 1}{4 x + 2} |

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

1103082701

Level:

Function

f

is given completely by the graph. Identify which of the following statements is false.

f (x) = \frac{1}{x}; x \in [- 2; - 0.5]

f (x) = | - \frac{1}{x} |; x \in [- 2; - 0.5]

f (x) = \frac{1}{| x |}; x \in [- 2; - 0.5]

f (x) = - \frac{1}{x}; x \in [- 2; - 0.5]

1103102304

Level:

Function

f

is given completely by the graph. Which of the following statements is false?

f (x) = \frac{| x |}{x}, x \in [- 5; 0) \cup (0; 5]

f (x) = | \frac{| x |}{x} |, x \in [- 5; 0) \cup (0; 5]

f (x) = 1, x \in [- 5; 0) \cup (0; 5]

f (x) = \frac{x}{x}, x \in [- 5; 0) \cup (0; 5]

1103124502

Level:

Identify which of the graphs below represents the function

f (x) = | \frac{1 - 2 x}{x - 4} |; x \in [- \frac{5}{2}; \frac{5}{2}]

1103124602

Level:

Let

f (x) = \frac{x^{2} - x - 6}{x^{2} - 9}

. One of the following pictures shows a part of the graph of

f

. Choose the picture.

2010009904

Level:

A part of the graph of the function

f (x) = \frac{- 3}{x}

is shown in the picture. Identify which of the following statements is true.

The function

g

defined by

g (x) = - | f (x) |

is bounded above.

The function

m

defined by

m (x) = | f (x) |

is bounded above.

The function

h

defined by

h (x) = - f (x)

is bounded below.

The function

f

is bounded below.

2010017301

Level:

Identify which of the given functions is odd.

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

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

g (x) = 2 x^{3} - 16

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

2010017302

Level:

Find the interval where the function

f (x) = - | 2 + \frac{1}{x} |

is a decreasing function. The function

f

is graphed in the picture.

[- \frac{1}{2}; 0)

(- \infty; 0)

[- \frac{1}{2}; \infty)

(- \infty; - \frac{1}{2})

2010017304

Level:

Consider the functions

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

y

-axis.

k = \frac{2}{3}

k = \frac{3}{2}

k = - \frac{2}{3}

k = - \frac{3}{2}

1003118306

1003118307

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1103102304

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1103124602

2010009904

2010017301

2010017302

2010017304

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