Which of the following graphs are graphs of polynomials Click on each graph to v

Question

Which of the following graphs are graphs of polynomials Click on each graph to view a larger version. Enter Ynte boxes corresponding to graphs of polynomials Enter N in the boxes corresponding to graphs of functions that are not polynomials Use the Leading Coetficient Test to determine the end behavior of the graphs of the folowing polynomial functions Use this end behavior to match the polynomial function with graph (Graphs are not to scale, but there is only one possble answer for each function) Click on each graph to view a larger version. Enter the letter of the corresponding graph for each function below f(r) 19ri 1

Explanation / Answer

1. A. f(x) = 8(x-5)2 . Here, f(x) = 8(x2-10x+25) = 8x2- 80x +200 is an even function with a positive leading coefficient. Further, f( x) as x ±. The graph is a parabola with vertex at (5,0) which rises upwards. It matches with graph A.

B. f(x) = 6x3 -6x2. Here, f(x) is an odd function with a positive leading coefficient. Further, 6x3 -6x2 = 6x2(x-1), hence there are two zeros at x = 0 and a third zero at x = 1. The graph of f(x) matches with graph C.

C. f(x)= -7x3-12x2 +12x-2 is an odd function with a negative leading coefficient. Further,f(x)+, as x and f(x), as x+. The graph matches with graph D.

D. f(x) = -19x4+11x2 = x2(-19x2+11). is an even function with a negative leading coefficient.f(x), as x±. Further, there are 2 zeros at x = 0. The graph matches with graph B.

2. 1) and 2) are graphs of polynomial functions.

3) The graph is not clear, but it appears that it is a graph oh a piecewise function. Hence N.

4). The graph is not clear, but it appears to be that of a linear function which is not defined for negative values of x. Hence N.

3. 1). f(x) = -2x11 +6x10 -2x9 -4x-2. Here, f(x) is an odd function with a negative leading coefficient.   Hence f(x)+, as x and f(x), as x+. Thus, the graph rises to the left and falls to the right. Option C is the correct answer.

2). f(x) = 5x10 -2x9 +3x8 -3x +2. Here, f(x) is an even function with a positive leading coefficient. Hence f(x) +, as x ±. Therefore, the graph rises to the left and also rises to the right. Option C is the correct answer.

3) f(x) = -5x4 -2x3+7x2 +6x + 4. Here, f(x) is an even function with a negative leading coefficient. Hence f(x), as x± . Therefore, the graph falls to the left and also falls to the right. Option C is the correct answer.

4). f(x) = 2x9 -8x8 +9x7 +8x -2. Here, f(x) is an odd function with a positive leading coefficient. Hence, f(x), as x and f(x)+, as x+. Therefore, the graph falls to the left and rises to the right. Option D is the correct answer.

  

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.