Question

Consider the leading term of the polynomial function. What is the end behavior of the graph?
-3x5 + 9x4 + 5x3 + 3
a. The leading term is -3x5. Since n is odd and a is negative the end behavior is up and up
b. The leading term is -3x5. Since n is odd and a is negative the end behavior is down and down
c. The leading term is -3x5. Since n is odd and a is negative the end behavior is up and down
d. The leading term is -3x5. Since n is odd and a is negative the end behavior is down and up

Answer 1

I don't know. Maybe accessdenied can help.

Answer 2

@AccessDenied need ur help please

Answer 3

End behavior is determined in a polynomial by the highest degree term, or in other words the \(ax^n\) whose value of n is largest.

Do you recall any statements about how polynomial degree and coefficients affect this?

Answer 4

c

Answer 5

For example, think about these simpler functions: y = x, y = -x, y = x^2, and y = -x^2.
Odd powers tend to have a different right-end behavior from right-end behavior.
Even powers tend to have the same end behavior both directions because you are inevitably squaring any negative or positive value. \( x^{2n} = (x^2)^n \)
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C. appears to be correct, then, because the left-end behavior is getting larger positive, and the right-end is getting larger negative. Think about putting in large positive or negative numbers in the leading term; -3( -big number)^3 = + 3 (big numbers). The odd power conserves the sign.

Answer 6

idifferent right-end behavior from left-end behavior. **