Let a, b, and c be real numbers where a b c 0. which of the following functions could represent the graph below? f(x) = x2(x – a)2(x – b)4(x – c) f(x) = x3(x – a)3(x – b)(x – c)2 f(x) = x4(x – a)(x – b)3(x – c)3 f(x) = (x – a)2(x – b)(x – c)6

Step-by-step explanation:

From the graph, we can conclude the following points:

1. Number of zeros = 4 ( As the graph intersects or touches the x axis at 4 points.)

2. Number of turning points are 6. ( As there are 3 minimums and 3 maximums)

3. Number of zeros with even powers are 3. ( As the graph touches the x axis at 3 points)

Among all the four options, only the first option fulfills all the above points.

The above function has 4 zeros at

The above function has 3 even zeros

Now, number of turning points for the above function is given as:

Turning points = Number zeros + Number of even zeros - 1 = 4 + 3 - 1 = 6

Therefore, the correct option is option 1.

a is the correct answer.

f(x ) (x -a )2(x-)(x - c)

in the graph you can see that the graph of the given function has four x-intercepts. one of them is 0 (choice d is incorrect, because factor x is not present), and denote rest as a, b, c, consecutively. at points 0, a and c function doesn't change sign, this means that factors x, (x-a), (x-c) have even degrees (choices b and c are incorrect, because in these options just two or three factors have odd degree). at point b function changes values from negative to positive, then the factor (x-b) should have odd degree. choice a is correct choice.

Its A

Step-by-step explanation: