Function Notation Worksheet

**Page 1**

1.

Which of the following is true about the given functions $f$ ($x$) = $\frac{{x}^{2}+x-2}{x-1}$ and $g$ ($x$) = $x$ + 2?

a. | Both functions $f$($x$) = $g$($x$) + 1 | ||

b. | Both functions $f$($x$), $g$($x$) are identical | ||

c. | Both functions $f$($x$), $g$($x$) are not identical | ||

d. | Both functions $f$($x$), $g$($x$) have the same domain |

Clearly, the function

For all real

[Use polynomial division.]

The function

So,

Though both the functions have the same definitions , they are not identical as they have different domains.

Correct answer : (2)

2.

Choose the domain of the function $f$ ($x$) = $\frac{1}{x+16}$.

a. | All real $x$ except - 16 | ||

b. | All real $x$ except 16 | ||

c. | All real vaues | ||

d. | All real $x$ except - 17 |

[

Correct answer : (1)

3.

Which of the following transformations have to be applied to the graph of reciprocal function $f$ ($x$) = $\frac{1}{x}$ to get the graph of $g$ ($x$) = $\frac{2}{x+6}$?

a. | Translation to the left by 2 units and a vertical stretch by a factor of 6. | ||

b. | Translation to the left by 6 units and a vertical stretch by a factor of 6. | ||

c. | Translation to the left by 6 units and a vertical stretch by a factor of 2. | ||

d. | Translation to the left by 2 units and a vertical stretch by a factor of 2. |

= 2 (

= 2 ·

The graph of

Correct answer : (3)

4.

Which of the following transformations have to be applied to the graph of reciprocal function $f$ ($x$) = $\frac{1}{x}$ to get the graph of $g$ ($x$) = $\frac{5x-29}{x-6}$?

a. | Translation to the right by 5 unit and then translation vertically up by 6 units. | ||

b. | Translation to the right by 6 unit and then translation vertically up by 5 units. | ||

c. | Translation to the right by 6 unit and then translation vertically up by 6 units. | ||

d. | Translation to the right by 5 unit and then translation vertically up by 5 units. |

[Use polynomial division.]

So,

The graph of

Correct answer : (2)

5.

Which of the following is the vertical asymptote of $h$($x$) = $\frac{{x}^{2}+36}{x}$?

a. | $y$ = 0 | ||

b. | $x$ = - 36 | ||

c. | $x$ = 36 | ||

d. | $x$ = 0 |

[Find the zeros of the denominator.]

The vertical asymptote is the line

[For the graph of a rational function vertical asymptotes occur at the zeros of the denominator, which are not the zeros of the numerator.]

Correct answer : (4)

6.

Find the $x$ - intercept of the graph of $f$ ($x$) = $\frac{{x}^{2}-9x+20}{x+5}$.

a. | (4 , 0) and (- 5, 0) | ||

b. | (- 4 , 0) and (- 5, 0) | ||

c. | (- 4, 0) and (5, 0) | ||

d. | (4 , 0) and (5, 0) |

[Solve the numerator for the zeros.]

(

[Factor.]

The zeros of the numerator are

So, the

[The

Correct answer : (4)

7.

Which of the following would be the end behavior asymptote of $y$ = $\frac{{x}^{2}+25}{x-5}$ ?

a. | $y$ = $x$ + 25 | ||

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

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

d. | $y$ = 5$x$ |

[Use polynomial division.]

Hence, the end behaviour asymptote of the graph of the given function is

[The end behaviour asymptote of

Correct answer : (3)

8.

Which of the following transformations have to be applied to the graph of reciprocal function $f$ ($x$) = $\frac{1}{x}$ to obtain the graph of $g$ ($x$) = $\frac{88-9x}{x-10}$?

a. | Translation to the right by 10 units followed by a reflection about $y$-axis. | ||

b. | Translation to the right 10 units, vertical stretch by a factor of 10, a reflection across $x$ - axis and translation vertically down by 9 units. | ||

c. | Translation to the right 10 units, vertical stretch by a factor of 2 , a reflection across $x$ - axis and translation vertically down by 9 units. | ||

d. | Translation to the right 10 units, vertical stretch by a factor of 2 , a reflection across $x$ - axis and translation vertically down by 2 units. |

[Use polynomial division.]

= - 9 - 2(

= - 9 - 2

The graph of

Correct answer : (3)

9.

Use the graph of the function $f$ ($x$) to evaluate $\underset{x\to \mathrm{\infty}}{\mathrm{lim}}$ $f$ ($x$).

a. | 3 | ||

b. | ∞ | ||

c. | -∞ |

[From the graph.]

Hence,

Correct answer : (1)

10.

Use the graph of the function $f$ ($x$) to evaluate $\underset{x\to {-2}^{-}}{\mathrm{lim}}f(x)$.

a. | -∞ | ||

b. | ∞ | ||

c. | 3 |

As

[From the graph.]

Hence,

Correct answer : (3)