Symmetry and Transformations Worksheet

**Page 1**

1.

Use function notation to represent the transformation of the graph of $h$($x$) shown with dotted lines.

a. | $\frac{1}{2}$$h$($x$) | ||

b. | $h$($x$) + 2 | ||

c. | $h$($x$) - 2 | ||

d. | 2$h$($x$) | ||

e. | $h$($x$) |

So, the function notation representing the transformation of

Correct answer : (2)

2.

Use function notation to represent the transformation of the graph of $f$($x$) shown with dotted lines.

a. | $f$ ($x$ + 4) | ||

b. | $\frac{1}{4}$ $f$ ($x$) | ||

c. | $f$ ($x$) + 4 | ||

d. | 4 $f$ ($x$) | ||

e. | $f$ (4$x$) |

So, the function notation representing the transformation of

Correct answer : (4)

3.

Use function notation to represent the transformation of the graph of $f$ ($x$) shown with dotted lines.

So, the function notation representing the transformation of

Correct answer : (0)

4.

Describe the graph of $\frac{1}{5}$ $g$($x$) that can be obtained by tranformation of the graph of $g$($x$).

a. | Horizontally stretching by a scale factor of 5 | ||

b. | Vertically shifting $\frac{1}{5}$ units upward | ||

c. | Horizontally compressing by a scale factor of $\frac{1}{5}$ | ||

d. | Vertically compressing by a scale factor of $\frac{1}{5}$ | ||

e. | Vertically stretching by a scale factor of 5 |

Correct answer : (4)

5.

Describe the graph of $h$($\frac{1}{3}$$x$) that can be obtained by tranformation of the graph of $h$($x$).

a. | Vertically stretching by a scale factor of 3 | ||

b. | Horizontally shifting 3 units upward | ||

c. | Horizontally stretching by a scale factor of $\frac{1}{3}$ | ||

d. | Vertically compressing by a scale factor of $\frac{1}{3}$ | ||

e. | Horizontally stretching by a scale factor of3 |

Correct answer : (3)

6.

Describe the graph of $f$ ($x$ - 10) that can be obtained by the tranformation of the graph of $f$ ($x$).

a. | Horizontal shift of 10 units to the right | ||

b. | Vertical shift of 10 units upward | ||

c. | Horizontal shift of 10 units to the left | ||

d. | Vertical shift of 10 units downward | ||

e. | Horizontally compressing by a scale factor of 10 |

Correct answer : (1)

7.

Given the function $h$($x$), explain how the transformation $h$(- $x$) changes the graph of $h$($x$).

a. | Translate 1 unit down | ||

b. | Reflection about the origin | ||

c. | Reflection over the $x$-axis | ||

d. | Translate 1 unit to the left | ||

e. | Reflection over the $y$-axis |

Correct answer : (5)

8.

Use function notation to represent the transformation of the graph of $f$($x$) shown with dotted lines.

a. | 4$f$ ($x$) | ||

b. | $f$($x$ + 4) | ||

c. | $\frac{1}{4}$ $f$($x$) | ||

d. | $f$(4$x$) | ||

e. | $f$($x$) + 4 |

Correct answer : (1)

9.

Which of the following is true for the graph of even function?

a. | symmetric with respect to the origin | ||

b. | symmetric with respect to the $x$-axis | ||

c. | symmetric with respect to the both origin and $y$-axis | ||

d. | symmetric with respect to the $y$-axis | ||

e. | symmetric with respect to both $x$ and $y$-axes |

The graph of an even function is symmetric with respect to the

Correct answer : (4)

10.

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

a. | $f$($x$) is an odd function | ||

b. | $f$($x$) is an even function | ||

c. | $f$($x$) is symmetric about origin | ||

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

e. | Both A and C |

So,

[If

Correct answer : (5)