Introduction to Rational Functions

Intro to Rational Functions

Unit 4

Rational numbers.

• A rational number is the quotient of two integers.

• For example:

   $\frac{4}{5}\ or\ 6\ \left(this\ is\ technically\ \frac{6}{1}\right)$  

Multiple Choice

Is 6/2 a rational number?

• Yes

• No

Multiple Choice

Is

$$\frac{\pi}{5}$$  a rational number?

• Yes 

• No

Multiple Choice

Is 4.5/2 a rational number?

• Yes

• No

Rational functions.

• Functions that are made up of algebraic fractions where both the numerator and denominator are polynomials.

• The coefficients of the polynomial must be rational.

• 
  
   $f\left(x\right)=\frac{x^2+1}{x^3+5},\ f\left(x\right)=\frac{x^5+3x^4+4x^2+55}{x^6+x^4+33x^3+21x^2+4},\ f\left(x\right)=\frac{1}{x}$  
  

Multiple Choice

Is

$$f\left(x\right)=\ \frac{\pi+5x}{x^2+1}$$   a rational function?

• Yes 

• No

Multiple Choice

Is

$$f\left(x\right)=\frac{x}{x+3}$$  a rational function?

• Yes

• No

Open Ended

What would happen if

$$x=-3\$$  in  $$f\left(x\right)=\frac{x}{x+3}$$  ?