Question

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?

Answer 1

@campbell_st

Answer 2

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

Answer 3

well hmmm
\(\bf f(x)=\cfrac{2x^2+5x-12}{x+4}\)

anyway to factor say \(\bf 2x^2+5x-12?\)

Answer 4

(x+4)(2x-3)

Answer 5

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?

Answer 6

(-4,-11)

Answer 7

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

Answer 8

ok. I agree.

Answer 9

:)

Answer 10

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

Answer 11

3

Answer 12

??

Answer 13

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

Answer 14

Gotcha :) Thanks once again

Answer 15

yw

Answer 16

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