Find the end behavior, Even, ODD or neither, and Leading Coefficient Of the below graph.

Question

Image Here: https://ibb.co/qrM6TBK

Answer 1

This is an even degree, with a leading coefficient that's negative, so

1. the end behavior is:
2. as f(x)→-∞, x→-∞, and f(x)→-∞, x→+∞
3. This is an even function since f(-x) = f(x) - (symetrical around the y axis)
4. Leading coefficient - we know it is negative, since it is opening downward. To find the value of the leading coefficient, use the n+1 principle and pick out the 5 obvious coordinates from the graph you linked to. (-2,-3), (-1,2), (0,0), (1,2), (2,3) are the points I think are the obvious ones. Generate 5 equations, 5 unknowns from that using ax⁴ + bx³ + cx² +dx + e = y, then use the matrix function on your calculator (I will assume you know how to do that); to solve for a, b, c, d, e (coefficients). I get:
5. a = (-4/3), b = (-5/6), c = (10/3), d = (5/6), e = 0 These are the leading coefficients.
6. Full equation: f(x) = (-4/3) x⁴ + (-5/6)x³ + (10/3)x² +(5/6) = y

I hope that helps. If the last question is just asking about the sign of the leading coefficient, you can ignore the last part in finding the coefficient values... :-)