Problem

Describe the end behavior of the graph of the polynomial function.
\[
f(x)=2 x^{6}-3 x^{4}+x^{2}-5
\]

Choose the correct answer below.
A. $\downarrow \downarrow$
c. 2
B.
D.

Answer

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Answer

Final Answer: The end behavior of the graph of the polynomial function is \( \boxed{\uparrow \uparrow} \)

Steps

Step 1 :The end behavior of a polynomial function is determined by the degree and the leading coefficient of the polynomial. The degree of the given polynomial function is 6, which is an even number, and the leading coefficient is 2, which is positive.

Step 2 :For a polynomial with an even degree and a positive leading coefficient, as x approaches positive infinity, f(x) approaches positive infinity, and as x approaches negative infinity, f(x) also approaches positive infinity.

Step 3 :So, the end behavior of the graph of the polynomial function is 'upwards on both ends'.

Step 4 :Final Answer: The end behavior of the graph of the polynomial function is \( \boxed{\uparrow \uparrow} \)

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