Question

Use the leading coefficient and the degree of the polynomial function to determine the end behavior of the graph. f(x) = 3x^2 - 3x^5 - 14x - 2x^3 - 5

leading coefficient:
degree:
end behavior left or right side:

Answer 1

end behavior on left: function goes to + infinity

end behavior on the right: function goes to - infinity

Explanation:

You look at the highest powered x term.

You look at the highest powered x-term which is - 3x^5. The polynomial will begin and end the same way a -x^5 curve begins and ends.

end behavior on the left side (as x approaches negative infinity), y values approach positive infinity. You can substitute negative values of x (-1, -5, -10, -100 . . .) in - 3x^5 and you will get increasing positive values for y as you use x values that approach negative infinity).

end behavior on the right side (as x approaches positive infinity), y values approach negative infinity. Substitute positive values for x (1, 10, 100, 1,000 . . .) in - 3x^5 and you will get decreasing negative values for y.