What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?

Question

anonymous · Answer

attachment

mathmale · Answer

Which is the dominant term of the given polynomial?

mathmale · Answer

Why?  Is the power of that term even or odd?

anonymous · Answer

even

jhonyy9 · Answer

3x^4(x^2 +10x +25)

3(-)^4(-)^2 +10(-) +25)

so than you see indifferent than will be x minus or plus will result f(x) positive

@mathmale you dont think the same please ?

anonymous · Answer

so answer is c

mathmale · Answer

Determining whether or not the order of this polynomial is even or odd is the first step.  @e2020army:   what other reasons have you for choosing "c" as your answer?

mathmale · Answer

You might want to graph the even function  y = x^2.   Describe its end behavior, please.
Graph the even function y=x^4, and describe its end behavior

Doing these 2 things will probably point you towards the correct answer.

mikwind · Answer

Rewrite the equation in this form:  $$y=x^6(3+\frac{ 30 }{ x }+\frac{ 75 }{ x^2 })$$ , what happens when x becomes very large, what happens when x becomes or very negative

mikwind · Answer

Hint: $$\lim_{x \rightarrow \pm  \infty}\frac{ a }{ x } $$ goes to 0

mathmale · Answer

@e2020army:  It'd be polite to inform your helpers if you're leaving a discussion in mid-stream.