anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
sorry i forgot your name :) so i couldn't tag you
jdoe0001
  • jdoe0001
well hmmm \(\bf f(x)=\cfrac{2x^2+5x-12}{x+4}\) anyway to factor say \(\bf 2x^2+5x-12?\)

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anonymous
  • anonymous
(x+4)(2x-3)
jdoe0001
  • 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?
anonymous
  • anonymous
(-4,-11)
jdoe0001
  • 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
anonymous
  • anonymous
ok. I agree.
jdoe0001
  • jdoe0001
:)
anonymous
  • anonymous
so the zero would be at 3/2, and 0? And discontinuity would be (-4,-11)
anonymous
  • anonymous
3
anonymous
  • anonymous
??
jdoe0001
  • jdoe0001
the zero is at x= 3/2 and the discontinuity is at x = -4
anonymous
  • anonymous
Gotcha :) Thanks once again
jdoe0001
  • jdoe0001
yw
anonymous
  • anonymous
Don't kill me but I have another, I'll tag u again :)

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