Rational functions

2010017305

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} \geq k_{2}

k_{1} = k_{2}

The relationship between

k_{1}

and

k_{2}

cannot be determined from the picture.

2110017303

Level:

Let

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

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

f

. Choose the picture.

9000002908

Level:

Find the intervals where the function

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

is an increasing function. The function

f

is graphed in the picture.

[- 1; 0)

(- \infty; 1]

(- \infty; 0)

(0; \infty)

9000007603

Level:

Find the domain of the function

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

R ∖ {2}

R ∖ {- 2}

R ∖ {4}

R ∖ {1}

R

9000007604

Level:

Find the domain of the function

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

R

R ∖ {- 1}

R ∖ {- 1; 1}

R ∖ {- 1; 0; 1}

R ∖ {1}

9000007605

Level:

Find the domain of the function

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

R ∖ {- 1; 1}

R ∖ {- 1}

R ∖ {- 1; 0; 1}

R ∖ {1}

R

9000007608

Level:

Find the range of the function

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

(1; \infty)

R

R ∖ {1}

(0; \infty)

R ∖ {2}

9000007609

Level:

Find the range of the function

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

(1; 2]

R ∖ {- 1; 1}

(0; \infty)

(1; \infty)

R

9000007610

Level:

Find the range of the function

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

(1; \infty)

R ∖ {- 1}

(0; \infty)

R ∖ {- 1; 1}

R

9000008008

Level:

Given the functions

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

find the value of the parameter

k \in R ∖ {0}

which ensures

g (2) = 2 f (- 2) .

4

2

- 1

- 2

2010017305

2110017303

9000002908

9000007603

9000007604

9000007605

9000007608

9000007609

9000007610

9000008008

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