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• A function  f  which is written of the form $\frac{P(x)}{Q(x)}$where $P(x)$ and $Q(x)$ are polynomials, $Q(x) \ne 0$  is a rational function.
• Domain of $f(x) = \frac{P(x)}{Q(x)}$ is the set of real numbers suchthat $Q(x) \ne 0$
• Procedures following to draw graph of $f(x) = \frac{N(x)}{D(x)}$, where $N(x)$= numerator, $D(x)$ =  denominator are polynomials.
• given a rational function $f(x) = \frac{P(x)}{Q(x)}$:the line $x = a$ is a vertical assymptote of the graph of $f$ if $f(x) \to \infty$ or $f(x) \rightarrow -\infty as x \to a$ either from the right or from the left.
• given a rational function $f(x) = \frac{P(x)}{Q(x)}$:the line $y = b$ is a horizontal assymptote of the graph of $f$ if $f(x) \to b as x \to \infty$ or $x \rightarrow -\infty$

• Let A be the time taken to complete a certain job by worker one and B be the time taken by the second worker to complete the job.
• Rate of accomplishing the job of the first worker is equal to $\frac{1}{A}$   and rate of second worker is equal to $\frac{1}{B}$ Rate of working together is $\frac{1}{A}+\frac{1}{B}=\frac{1}{x}$  , if $x$is the time it takes to complete the job together.
• Let $x$, $y$ be variables and $K$ be the constant: Direct variation $y = Kx$  means x and y are directly across from each other.Inverse variation$y = \frac{K}{x}$ means that x is inverted on the other side of y. Joint variation$y = Kwx$  means w and x jointly are directly varied withy