Complete the table of values for the function y = 1 x . x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y - 1 8 - 2

Given: y = 1 x (i) When x = - 4 , y = 1 - 4 (ii) When x = - 2 , y = 1 - 2 (iii) When x = - 1 , y = 1 - 1 = - 1 (iv) When x = - 1 4 , y = 1 - 1 4 = - 4 (v) When x = - 1 8 , y = 1 - 1 8 = - 8 (vi) When x = 1 8 , y = 1 1 8 = 8 (vii) When x = 1 4 , y = 1 1 4 = 4 (viii) When x = 1 2 , y = 1 1 2 = 2 (ix) When x = 1 , y = 1 1 = 1 (x) When x = 2 , y = 1 2 (xi) When x = 4 , y = 1 4 (xii) When x = 8 , y = 1 8 Hence, the table is as follows: x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y - 1 8 - 1 4 - 1 2 - 1 - 2 - 4 - 8 8 4 2 1 1 2 1 4 1 8

Draw the graph for the function y = 1 x for values of x from - 8 to 8 .

Given: y = 1 x The value table is as follows: x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y - 1 8 - 1 4 - 1 2 - 1 - 2 - 4 - 8 8 4 2 1 1 2 1 4 1 8 Hence, the graph is as follows:

Complete this table of values for y = - 1 x for values of x between - 8 and 8 x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y

Given that, we have: y = - 1 x To find values of y : We can substitute the values of x in given rational expression to find the respective values of y . The values table is as follows: x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y 1 8 1 4 1 2 1 2 4 8 - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8

Draw the graph of y = - 1 x for values of x between - 8 and 8 . x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y

Given that, we have: y = - 1 x To find values of y : We can substitute the values of x in given rational expression to find the respective values of y . The values table is as follows: x - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 1 8 1 4 1 2 1 2 4 8 y 1 8 1 4 1 2 1 2 4 8 - 8 - 4 - 2 - 1 - 1 2 - 1 4 - 1 8 Thus, the graph of the given rational function can be drawn by using the above table. The graph of y = - 1 x is

State the domain and range of the function: y = - 1 x .

Given that, the rational function is y = - 1 x The domain of a function f x is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. Thus, clearly, the function is not defined when x ≠ 0 So, the domain of the function is x ∈ R , x ≠ 0 Similarly, x = - 1 y Here, also, the function is not defined when y ≠ 0 So, the range of the function is y ∈ R , y ≠ 0 .

State the equation of the horizontal and vertical asymptotes of the function y = - 1 x . How do they relate to the domain and range?

Given that, the rational function is y = - 1 x The equation of the horizontal asymptote: y = 0 And the equation of the vertical asymptote: x = 0 . The domain of a function f x is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. Thus, clearly, the function is not defined when x ≠ 0 So, the domain of the function is x ∈ R , x ≠ 0 Similarly, x = - 1 y Here, also, the function is not defined when y ≠ 0 So, the range of the function is y ∈ R , y ≠ 0 . Thus, clearly, a function to be defined to find a domain or range and to find asymptotes: A vertical asymptote is a vertical line at which the function is undefined. The graph of a function cannot touch a vertical asymptote, and instead the graph either goes up or down infinitely. A horizontal asymptote is a horizontal line that the graph of the function approaches as x increases in the positive or negative direction. Unlike vertical asymptotes, it is possible to have the graph of a function touch its horizontal asymptote.

E M B I B E

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Introducing rational functions>Q ●

EASY

MYP:4-5

IMPORTANT

Earn 100

What is rational function?

Important Questions on Graphs of Rational Functions

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Introducing rational functions>Q ●

How are asymptotes linked to domain and range?

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Exploration 1>Q 1

Complete the table of values for the function $y = \frac{1}{x}$ .

$x$	$- 8$	$- 4$	$- 2$	$- 1$	$- \frac{1}{2}$	$- \frac{1}{4}$	$- \frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{2}$	$1$	$2$	$4$	$8$
$y$	$- \frac{1}{8}$				$- 2$

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Exploration 1>Q 2

Draw the graph for the function $y = \frac{1}{x}$ for values of x from $- 8$ to $8$ .

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Exploration 1>Q 3

Explain what happens as $x$ gets closer to $0$ . Think about what happens for both positive and negative values of $x$ that approach $0$ for the following function:

$y = \frac{1}{x}$

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Exploration 2>Q 1

Complete this table of values for $y = - \frac{1}{x}$ for values of $x$ between $- 8 and 8$

$\begin{array}{l} x & - 8 & - 4 & - 2 & - 1 & - \frac{1}{2} & - \frac{1}{4} & - \frac{1}{8} & \frac{1}{8} & \frac{1}{4} & \frac{1}{2} & 1 & 2 & 4 & 8 \\ y \end{array}$

EASY

MYP:4-5

IMPORTANT

Extended MYP Mathematics A Concept based approach Years 4 & 5>Chapter 12 - Graphs of Rational Functions>Exploration 2>Q 1

Draw the graph of $y = - \frac{1}{x}$ for values of $x$ between $- 8 and 8$ .

$\begin{array}{l} x & - 8 & - 4 & - 2 & - 1 & - \frac{1}{2} & - \frac{1}{4} & - \frac{1}{8} & \frac{1}{8} & \frac{1}{4} & \frac{1}{2} & 1 & 2 & 4 & 8 \\ y \end{array}$