Answer:
Here's what I get
Step-by-step explanation:
a) Possible degree
This looks like the graph of a cubic equation.
ƒ(x) could be a third degree function.
b) Sign of leading coefficient
As x ⟶ ∞, ƒ(x) ⟶ ∞.
The leading coefficient must be positive.
c) Coordinates of maxima and minima
There is a local maximum at (-4, 0) and a local minimum at about (-1, -18.).
d) Coordinates of zeros
There are zeros at (-4, 0) and (1, 0).
e) Increasing and decreasing intervals
ƒ(x) is increasing in the intervals (-∞, -4) and (-1, ∞).
ƒ(x) is decreasing in the interval (-4, -1).
f) Negative intervals
The graph is negative in the intervals (-∞, -4) and (-4, ∞).
g) Possible factored form of equation
A cubic equation must have three roots. This function has a root at x = 1. Another is at x = -4. That root just touches the x-axis, so it must be degenerate (occur twice).
The factored form of the equation is
ƒ(x) = (x - 1)(x + 4)(x + 4)
h) End behaviour
ƒ(x) ⟶ -∞ as x ⟶ -∞ and ƒ(x) ⟶ ∞ as x ⟶ ∞
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