Which Of The Following Is True?

Question

anonymous · Answer

attachment

yrelhan4 · Answer

simplifying this would give you fx= 1/x+4.. what do you think?

anonymous · Answer

Wouldn't that make it A) X=4?

yrelhan4 · Answer

umm @amistre64 .. we would have to find the slope here?

amistre64 · Answer

no slope,  just the discontinuities

there is a jump and a vertical asymptote ... but the options are relating only to the va

yrelhan4 · Answer

only to the.. ? 
well you would be able to explain it better. i kinda got confused..

amistre64 · Answer

$$\frac{(x-4)}{x^2-16}$$
$$\frac{(x-4)}{x^2-4^2}$$
$$\frac{(x-4)}{(x-4)(x+4)}$$
$$\frac{(x-4)}{(x-4)}\frac{1}{(x+4)}$$
notice the left part "cancels" to 1 .... except at x=4,  if like parts cancel, we get a jump discontinuity.  it essentially is a hole in an otherwise perfect graph

notice the right part of it has a divide by zero issue when x=-4  in this case there is nothing to control it like the other side so it goes off into infinity and is called an asymptote

amistre64 · Answer

since we cannot use the values of 4 or -4 ... the zero options are pointless

anonymous · Answer

ok Thank You, From interpreting on what you said the correct answer choice is D, correct?

amistre64 · Answer

ill assume you meant C :)  theres is a VA at x=-4

anonymous · Answer

Whoops, silly me missed typed XP

amistre64 · Answer

good luck ;)

anonymous · Answer

Thanks :)