Properties of Function Worksheet

**Page 1**

1.

Choose the graph which represents a function.

a. | Graph -A | ||

b. | Graph -B | ||

c. | Graph -C | ||

d. | Graph -A & Graph -C |

[Vertical line test.]

A vertical line intersects the graph -B in two popints , so the given curve is not the graph of a function.

[Vertical line test.]

A vertical line intersects the graph-C in two points, so the given curve is not the graph of a function.

[Vertical line test.]

Correct answer : (1)

2.

What is the domain of the function defined by $h$($x$) = $\frac{1}{x}$ + $\frac{4}{x-4}$ ?

a. | (- ∞, ∞) | ||

b. | (- ∞, 0) U (4 , ∞) | ||

c. | (- ∞, 0) U (0, 4 ) U (4 , ∞) | ||

d. | (- ∞, 0] U [0, 4 ] U [4 , ∞) |

[The denominator of a fraction must not be zero.]

The domain is (-∞, 0) U (0, 4) U (4, ∞).

Correct answer : (3)

3.

Find the domain of the function defined by $g$($x$) = $\frac{\sqrt{36-x}}{(x+2)({x}^{2}+2)}$.

a. | (- ∞, - 2 ] U [- 2 , 36] | ||

b. | (- ∞, - 2 ) U (- 2 , 36] | ||

c. | [- ∞,- 2 ) U (- 2 , 36] | ||

d. | (- ∞, - 2 ) U (- 2 , ∞) |

[The denominator of a fraction must not be zero.]

36 -

[The expression under a radical must not be negative.]

[Solve.]

The domain is (-∞, - 2) U (- 2, 36].

Correct answer : (2)

4.

A relation $f$, which associates to each element of set A with a unique element of set B is called

a. | A mapping from A$\to $A | ||

b. | A function from B $\to $
A | ||

c. | Relation | ||

d. | Function from A$\to $B |

[Definition.]

Correct answer : (4)

5.

If $f$ is a function from set A to set B, then which of the following is correct?

a. | A is called domain of $f$ and B is called codomain of $f$ | ||

b. | A is called range of $f$ and B is called domain of $f$ | ||

c. | A is called codomain of $f$ and B is called domain of $f$ | ||

d. | A is called domain of $f$ and B is called range of $f$ |

Correct answer : (1)

6.

Which of the following formulas represents a function?

a. | $y$ = $\sqrt{x-4}$, [4, ∞) | ||

b. | $y$ = $x$ ^{2}± 3 | ||

c. | $y$ = $x$ + 5 | ||

d. | Both A and C |

Here

[Vertical line test.]

For the choice B:

For unique value of

[Vertical line test.]

For the choice C:

The graph of the given equation intersects vertical line at only one point with

[Vertical line test.]

Correct answer : (4)

7.

Choose the formula which is not a function.

a. | $x$ = 2 + $y$ | ||

b. | $y$ = $x$ + 5 | ||

c. | $y$ = $x$ ^{2} | ||

d. | $x$ = 2 $y$ ^{2} |

The graph has unique

[Vertical line test.]

For the choice B:

The graph has unique

[Vertical line test.]

For the choice C:

Here, the graph has two

[Vertical line test.]

For the choice D:

Here, the graph has two

[Vertical line test.]

Correct answer : (4)

8.

Find the domain of the function defined by $f$ ($x$) = $\sqrt{x+3}$.

a. | (- ∞, ∞) | ||

b. | (- ∞, 3 ] | ||

c. | [- 3 , ∞] | ||

d. | [ - 3 , ∞) |

[The expression under a radical sign should be positive.]

[Solve.]

Hence, the domain of

Correct answer : (4)

9.

What is the domain of the function $f$ ($x$) = $\frac{7}{{x}^{2}}$?

a. | [- ∞, 0) $\cup $ (0, ∞) | ||

b. | ( - ∞, 0) $\cup $ [ 0, ∞) | ||

c. | (- ∞, 0) $\cup $ (0, ∞) | ||

d. | (- ∞, 0] $\cup $ (0, ∞) |

0 is the only number, which is not in the domain of

[For all values of

Hence, the domain of

Correct answer : (3)

10.

Find the range of the function $f$($x$) = 9$x$^{3}

a. | [ - ∞, ∞] | ||

b. | (- ∞, ∞) | ||

c. | (- ∞, 0] | ||

d. | (- ∞, 0) U (0,∞) |

For all the real values of

So, the range of

Correct answer : (2)