Question

Let a, b, and c be real numbers where a =/b =/c =/ 0. Which of the following functions could represent the graph below?

Answer 1

Answer:

Its A

Step-by-step explanation:

Answer 2

Answer:

$f(x)=x^{2}(x-a)^{2}(x-b)^{4}(x-c)$

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.

$f(x)=x^{2}(x-a)^{2}(x-b)^{4}(x-c)$

The above function has 4 zeros at $x=0,a,b,c$

The above function has 3 even zeros $x^{2},(x-a)^{2},(x-b)^{4}$

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.