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I am confused because: g(x) = x^5-3x^2+1, a <0 makes the graph of choice 3 g (x) = x^3-3x^2+1, a>0 makes the graph of choice 3 f (x) = x^4-3x^2+1, a>0 makes the graph of choice 1 f (x) = x^6-3x^2+1, a<0 makes the graph of choice 1 Choices 1 and 3 look like it would go to + infinity Choices 2 and 4 look like it would go to - infinity
so let's look at graph 1... it looks like from what you said above you know you must have an even degree polynomial correct?
ok great so we have the options g(x)=ax^4 where a>0 or g(x)=ax^6 where a<0 as are only options
for the first graph
the trick is the negative and positive part
do you know what g(x)=x^4 and g(x)=-x^6 look like?
or at least their end behavior
I graphed it where does the g(x)=-x^6 come from the - sign?
I'm going to call them something different... g(x)=x^4 and f(x)=-x^6 --- g(100)=100^4 <--a really really big positive number where as f(100)=-100^6 <---a really really big negative number
your options says a<0
for the x^6 graph
a<0 means a is negative
a>0 means a is positive
oh I see > greater than which is + and < less than which is -
yep and I just chose 1 and -1 because they are the prettiest negative and positive numbers
f(x)=1x^4 and g(x)=-1x^6 look at graphs 1 and 4... which graph would be closer to something like f(x)=1x^4?
like just look at the end behavior or look at what f(100)=100^4 this means when you plug in a really large positive x value you are going to get a really ridiculous large positive output y value
graph 4 says well if I plug in a really big positive x value I'm going to get a really big negative y output
I got it now from top to bottom would be 2 1 4 3 the - in front of the x's was where I was making a mistake.
you got it
Thank you for taking the time to explain this to me I really appreciate it :)