Symmetry and Transformations Worksheet

**Page 2**

11.

Which of the following is true for the function $f$($x$) = $x$^{4} + 2$x$^{2} + 2 ?

a. | not symmetric | ||

b. | symmetric about the point $y$ = 2 | ||

c. | symmetric about origin | ||

d. | symmetric about $y$ - axis | ||

e. | an odd function |

[If

So,

[Even function is symmetric about

Correct answer : (4)

12.

Which of the following is true for the function $f$($x$) = $e$^{$x$2}?

I. symmetric about $y$ - axis

II. symmetric about origin

III. not symmetric

IV. $f$($x$) is an even function

V. $f$(- $x$) = - $f$($x$)

I. symmetric about $y$ - axis

II. symmetric about origin

III. not symmetric

IV. $f$($x$) is an even function

V. $f$(- $x$) = - $f$($x$)

a. | V only | ||

b. | II only | ||

c. | III only | ||

d. | I and IV | ||

e. | III and V |

Correct answer : (4)

13.

Which of the following is true for the function $f$($x$) = $\frac{1}{{x}^{2}+1}$ ?

I. $f$($x$) is an even function

II. symmetric about origin

III. not symmetric

IV. symmetric about $y$ - axis

V. $f$(- $x$) = - $f$($x$)

I. $f$($x$) is an even function

II. symmetric about origin

III. not symmetric

IV. symmetric about $y$ - axis

V. $f$(- $x$) = - $f$($x$)

a. | III and V | ||

b. | II only | ||

c. | III only | ||

d. | I and IV | ||

e. | V only |

[If

So,

Correct answer : (4)

14.

Which of the following is true for an odd function $f$($x$) ?

I. symmetric about origin

II. not symmetric

III. $f$(- $x$) = - $f$($x$)

IV. symmetric about $y$ - axis

V. $f$(- $x$) = $f$($x$)

I. symmetric about origin

II. not symmetric

III. $f$(- $x$) = - $f$($x$)

IV. symmetric about $y$ - axis

V. $f$(- $x$) = $f$($x$)

a. | I and III | ||

b. | IV and V | ||

c. | V only | ||

d. | II only | ||

e. | IV only |

The graph of an odd function is symmetric about origin.

Correct answer : (1)

15.

Which of the following is true for the function $f$($x$) = | $x$^{5} + 3$x$ | ?

I. symmetric about $y$ - axis

II. not symmetric

III. $f$($x$) is an even function

IV. $f$(- $x$) = - $f$($x$)

V. symmetric about origin

I. symmetric about $y$ - axis

II. not symmetric

III. $f$($x$) is an even function

IV. $f$(- $x$) = - $f$($x$)

V. symmetric about origin

a. | IV and V | ||

b. | II only | ||

c. | II and IV | ||

d. | I and III | ||

e. | IV only |

[If

So,

Correct answer : (4)

16.

Which of the following is true for the function $f$($x$) = $\frac{x}{{x}^{2}+1}$ ?

I. $f$($x$) is an odd function

II. symmetric about $y$ - axis

III. not symmetric

IV. symmetric about origin

V. $f$(- $x$) = $f$($x$)

I. $f$($x$) is an odd function

II. symmetric about $y$ - axis

III. not symmetric

IV. symmetric about origin

V. $f$(- $x$) = $f$($x$)

a. | I and IV | ||

b. | III only | ||

c. | II only | ||

d. | III and IV | ||

e. | V only |

So,

Correct answer : (1)

17.

Which of the following is true for the function $f$($x$) = $x$^{5} + $x$^{4} + $x$ + 1 ?

I. $f$($x$) is an even function

II. $f$($x$) is an odd function

III. $f$($x$) is neither even nor odd

IV. symmetric about origin

V. symmetric about $y$ - axis

I. $f$($x$) is an even function

II. $f$($x$) is an odd function

III. $f$($x$) is neither even nor odd

IV. symmetric about origin

V. symmetric about $y$ - axis

a. | IV only | ||

b. | V only | ||

c. | I and V | ||

d. | II and IV | ||

e. | III only |

The function is neither even nor odd.

Correct answer : (5)

18.

Which of the following is true for the function $f$($x$) = sin 2$x$ ?

I. $f$($x$) is an odd function

II. $f$($x$) is symmetric about origin

III. $f$($x$) is symmetric about $y$ - axis

IV. $f$($x$) is not symmetric

V. $f$(- $x$) = $f$($x$)

I. $f$($x$) is an odd function

II. $f$($x$) is symmetric about origin

III. $f$($x$) is symmetric about $y$ - axis

IV. $f$($x$) is not symmetric

V. $f$(- $x$) = $f$($x$)

a. | V only | ||

b. | I and II | ||

c. | III only | ||

d. | III and IV | ||

e. | IV only |

[If

So,

Correct answer : (2)

19.

Identify the figure that has the dotted line dividing the letter into two symmetrical halves.

a. | Figure 3 | ||

b. | Figure 2 | ||

c. | Figure 4 | ||

d. | Figure 1 |

Among the choices, the dotted line through the letter M divides it into two parts which are mirror images of each other.

The lines passing through the letters L, P, and Q do not divide them into two parts that would be mirror images of each other.

So, the dotted line through the letter M is a line of symmetry.

Correct answer : (2)

20.

Which of the figures (alphabets) has a line of symmetry?

a. | all the three figures | ||

b. | Figure 2, Figure 1 | ||

c. | Figure 1 | ||

d. | Figure 3, Figure 1 |

The dotted line for all the figures (alphabets) divides the figures into two parts, which are mirror images of each other.

So, the dotted lines for all the figures are the lines of symmetry.

Correct answer : (1)