Let a and b be real numbers where a=b=0. which of the following functions could represent the graph below? f(x)=x(x-a)^3(x-b)^3 f(x)=(x-a)^2(x-b)^4 f(x)=x(x-a)^6(x-b)^2 f(x)=(x-a)^5(x-b)

Option: b is the answer.

( f(x)=(x-a)^2(x-b)^4 )

Step-by-step explanation:

Clearly from the graph of the function we could see that zero is not a root of the polynomial function hence option (a) ( f(x)=x(x-a)^3(x-b)^3 ) and option (c) (  f(x)=x(x-a)^6(x-b)^2 )are discarded.

Now we will check for option (b) and option (d)

As the graph touches the x-axis at two point i.e. a and b that means that both the roots of the polynomial equation are of even degree.

Hence, the correct option is:

option: b ( f(x)=(x-a)^2(x-b)^4 ).

It can be deduced that the option that represents the graph is B. f(x)=(x-a)²(x-b)⁴

From the graph, a and b be real numbers where a=b=0. In this case, zero is not a root of the polynomial function

When the graph touches the x-axis at two point l, it implies that means that both the roots of the polynomial equation are of even degree.

In conclusion, the correct option is B.

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