Sketch the graph of polynomial function P(x)=14(x+1)3(x−3) make sure the graph shows all intercepts and exhibits the proper end behaviour.
The function has an even degree 4 and a positive leading coefficient. Thus, its end behaviour is y→∞ as x→−∞ and y→∞ as x→∞.
To solve for the x-intercept, we set y=0.
0=14(x+1)3(x−3)0=(x+1)3(x−3)
We have,
x=−1 and x=3
To solve for the y-intercept, we set x=0
y=14(0+1)3(0−3)y=14(1)3(−3)=−34
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