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Answer:
f(x) approaches infinity as x approaches infinity
Explanation:
Given
[tex]f(x) = 3x^6 + 30x^5+ 75x^4[/tex]
Required
The end behavior of the graph
We have:
[tex]f(x) = 3x^6 + 30x^5+ 75x^4[/tex]
The above expression implies that:
[tex]f(x) = 3x^6 + 30x^5+ 75x^4[/tex]
The leading coefficient is 3 (3 is positive)
And the degree of the polynomial is 6 (6 is even)
When the leading coefficient is positive and the degree is even; the end behavior of the function is:
[tex]x \to \infty[/tex]
[tex]f(x) \to \infty[/tex]