Question

Christi is doing her math homework. To receive full credit, she must answer this question: What key features are necessary—and how are the features used—to create the sketch of a polynomial function? What is Christi's correct answer, so she receives full credit for the question? Explain in complete sentences.

Answer 1

Explanation:

A) In general, you should first check for any holes in the graph by checking what x values return an undefined f(x).
B) Then solve for the vertical asymptote and horizontal asympotote. Remember that the line will approach but not intersect the asymptotes, so draw your function with the asymptotes as guides.

C) Then solve for the x intercepts and the y intercept. Begin at the x intercepts (if there are any. If there are no x intercepts, that means that the horizontal asymptote was probably at y=0

Answer 2

A polynomial equation has several variables (letters) and coefficients (numbers in it), for example:

3x^3 + 2x^2 + 1 = 0

The significant features of a polynomial equation comprise how it behaves for x<0 and x>0, the large negative and positive values of x, and how many zeroes it has (which is how many times it crosses the x axis (y=0) and where the zeroes are). Since the degree of the polynomial is the largest exponent (which is 3 in the above equation), you'll know that there are up to 3 different zeroes.