Question

How do you graph `F(x)=((4x^2)+8x-32)/((2x^2)-6x+4)`?

Answer 1

factorize the numerator and denominator separately

Explanation:

`F(x) = (4x^2+8x-32)/(2x^2-6x+4)`

can be factorized using rules for quadratic equation to simplify equation

Step 1 Taking 4 common from numerator and 2 from denominator

`F(x) = (4(x^2+2x-8))/(2(x^2-3x+2))`

Step 2 factorizing numerator and denominator

`F(x) = (4(x^2+ **4x-2x** -8))/(2(x^2- **2x-x** +2))`

in this step i have changed the middle term in both numerator and denominator in such a manner when you multiply 4x-2x you get -8 the third term in the numerator and similarly when you multiply -2x-x you get 2 the third term in the denominator

so now taking out common terms

`F(x) = (4(x(x+ 4)+(-2)(x+4)))/(2(x(x- 2)+(-1)(x +2)))`

`F(x) = (4(x-2)(x+4))/(2(x-1)(x -2))`

`F(x) = (2(x+4))/((x-1)`

graph{(2(x+4))/((x-1) [-infinity, infinity]}