Properties of functions

2000002403

Level:

Find the domain of the function

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

R ∖ {3}

R

(3; \infty)

(- 3; 3)

Level:

Decide which of the functions is even.

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

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

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

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

Level:

Decide which of the functions is odd.

f (x) = \frac{5}{x}

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

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

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

Level:

Let

f (x) = \frac{\sqrt{x - 3}}{x^{2} - 16}

. Which of the statements about the domain of the function

f

is true?

D (f) = [3; 4) \cup (4; \infty)

D (f) = (3; 4) \cup (4; \infty)

D (f) = (- \infty; - 4) \cup (3; 4)

D (f) = (- 4; 3) \cup (4; \infty)

Level:

In the following list identify an even function.

f (x) = | x | + 1

f (x) = | x + 1 |

f (x) = x + 1

f (x) = x

Level:

In the following list identify a function which is bounded below.

f (x) = (x + 4)^{2}

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

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

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

Level:

Identify a function which has a domain

(- \infty; - 2) \cup (3; \infty)

y = \sqrt{\frac{1}{(x + 2) (x - 3)}}

y = \sqrt{(x + 2) (x - 3)}

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

y = (x + 2) (x - 3)

y = \sqrt{(x - 2) (x + 3)}

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

Level:

In the following list identify an even function.

f (x) = | x |

f (x) = | x + 1 |

f (x) = x + 1

f (x) = x

Level:

In the following list identify an odd function.

f (x) = x^{3}

f (x) = | x^{3} |

f (x) = x^{4}

f (x) = | x^{4} |

Level:

In the following list identify a function which is not an odd function.

y = x + 3

y = x^{5}

y = \frac{3}{x}

y = x