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Homework Statement
lim
x-> -1
x^{3}-6x^{2}+11x - 6
x^{3}-4x^{2}+19x + 14
The limits of these polynomials depend on the values of x as it approaches positive or negative infinity. For x3-6x2+11x - 6, the limit as x approaches positive infinity is positive infinity and as x approaches negative infinity is negative infinity. For x3-4x2+19x + 14, the limit as x approaches positive infinity is positive infinity and as x approaches negative infinity is negative infinity.
To determine the limits of polynomials, you need to first simplify the polynomial by factoring and then analyze the highest degree term. The limit as x approaches positive or negative infinity will depend on whether the highest degree term is positive or negative, respectively.
The end behavior of a polynomial refers to the behavior of the polynomial as x approaches positive or negative infinity. The end behavior can be described as either approaching positive or negative infinity, approaching a finite value, or oscillating between positive and negative infinity.
To graph polynomials with limits, you can use the end behavior to determine the general shape of the graph. You can also plot a few points and use the symmetry of the graph to determine the rest of the points. Be sure to label the x and y-intercepts and any points of intersection with other functions.
Limits are important in polynomial functions because they can help us understand the behavior of the function as x approaches positive or negative infinity. This can give us insight into the overall shape and behavior of the polynomial and can be used to graph the function accurately.