Rational functions

9100003210

Level:

Identify a possible graph of the function

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

9100014204

Level:

Identify a possible graph for the function

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

9100014205

Level:

Identify a possible graph for the function

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

1003019401

Level:

Identify which of the given functions is even.

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

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

g (x) = \frac{x^{2}}{x + 1}

f (x) = \frac{x^{3}}{x^{2} - 5}

1003019402

Level:

Identify which of the given functions is neither even nor odd.

h (x) = \frac{x^{3} - 7}{2 x^{2}}

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

g (x) = \frac{5 x^{2} - 6}{x}

m (x) = \frac{x^{3}}{2 x^{2} + 5}

1003028401

Level:

Let

f (x) = \frac{3 x - 9}{x^{2} - 3}

. Which of the statements about the domain and the range of the function

f

is true?

3 \in D (f) \land 3 \in H (f)

3 \in D (f) \land 3 \notin H (f)

3 \notin D (f) \land 3 \in H (f)

3 \notin D (f) \land 3 \notin H (f)

1003028402

Level:

Let

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

. Which of the statements about the domain and the range of the function

f

is true?

- 2 \notin D (f) \land - 2 \in H (f)

- 2 \in D (f) \land - 2 \notin H (f)

- 2 \in D (f) \land - 2 \in H (f)

- 2 \notin D (f) \land - 2 \notin H (f)

1003030903

Level:

Identify which of the following functions is bounded below.

h (x) = \frac{2 x - 4}{x - 2}

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

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

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

1003118304

Level:

Identify which of the following functions is bounded.

h (x) = \frac{3 x - 6}{2 x - 4}

f (x) = \frac{3 x - 6}{2 x}

g (x) = 3 - \frac{6}{2 x}

m (x) = | \frac{4 x - 3}{2 x - 6} |

1003118305

Level:

Find the false statement about the function

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

The domain of the function

f

is the set

(- \infty; \frac{3}{2}) \cup (\frac{3}{2}; \infty)

The range of the function

f

is the interval

[0; \infty)

The function

f

has the minimum at

x = \frac{5}{9}

The function

f

is bounded below.

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9100014204

9100014205

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1003019402

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1003028402

1003030903

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1003118305

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