I have to take the graphs f(x)=x^4 and g(x)=3(x-2)^4 -4 and describe the end behaviors.
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is it as simple as stating the the end result is a vertical shift of 2 units to the right and a horizontal shift of 4 units down?
I get that the leading coefficient determines the end behavior, but how do I put it into words
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the leading coefficient in both curves is positive so since both are degree 4 polynomials they are both concave up... the coefficient of the leading term in g(x) is 3
so this is increasing quicker than f(x)
hope that helps
It does. this is what I came up with using both the worksheet and a bit of internet search.
both f(x) and g(x) have positive coefficients and are even degreed polynomials so the end results of both ends of the graphs will be going in the positive direction toward infinity
the worksheet says something about increasing without bounds as the other increases without bounds.... I'm confused by that.
is mean they approach infinity as x approaches infinity
and - infinity as x approaches - infinity.