## anonymous one year ago What is the discontinuity and zero of the function f(x) = the quantity of 2 x squared plus 5 x minus 12, all over x plus 4?

1. anonymous

@campbell_st

2. anonymous

sorry i forgot your name :) so i couldn't tag you

3. jdoe0001

well hmmm $$\bf f(x)=\cfrac{2x^2+5x-12}{x+4}$$ anyway to factor say $$\bf 2x^2+5x-12?$$

4. anonymous

(x+4)(2x-3)

5. jdoe0001

hmm,, right so $$\bf \cfrac{2x^2+5x-12}{x+4}\implies \cfrac{\cancel{(x+4)}(2x-3)}{\cancel{(x+4)}}$$ so.. that's the graph, just a LINEar function, thus is just a line now, where is it discontinued, where does the line have a gap?

6. anonymous

(-4,-11)

7. jdoe0001

so.. let's us check if say we set x = -4 so...on the original equation we'd have $$\bf \cfrac{2x^2+5x-12}{x+4}\qquad {\color{brown}{ x=4}}\implies \cfrac{2{\color{brown}{ -4}}^2+5{\color{brown}{ -4}}-12}{{\color{brown}{ -4}}+4}$$ the denominator turns to 0, thus making the fraction undefined, thus the gap at that value, when x= -4

8. anonymous

ok. I agree.

9. jdoe0001

:)

10. anonymous

so the zero would be at 3/2, and 0? And discontinuity would be (-4,-11)

11. anonymous

3

12. anonymous

??

13. jdoe0001

the zero is at x= 3/2 and the discontinuity is at x = -4

14. anonymous

Gotcha :) Thanks once again

15. jdoe0001

yw

16. anonymous

Don't kill me but I have another, I'll tag u again :)