Question

The function f(x) has four distinct roots. Which of the following graphs can represent f(x)?

Answer 1

The number of times the graph of the equation is intersecting the x axis is the number of the solution of the f(x) = 0.

Complete step-by-step answer:
The number of times the graph is intersecting the x axis ,that is the number of solutions of the equation f(x)=0.
Now if we try to analyze the options given in the question, we can see,

In option A, As we can see, the graph of the equation intersects the x axis twice.
In option B, as we find, the graph of the equation intersects the x axis thrice.
In option C, we see, the graph of the equation intersects the x axis twice.
In option D, we find, the graph of the equation intersects the x axis four times.

So, at the end we can see that the graphs given to us intersects the x axis in some way. The number of times it is intersecting the x axis is the number of solutions of that equation or the given graph.
So, the graph of option D among the following options represents our desired graph f(x) as it will have four solutions.

Note: We can see in the graph of option B, the graph of the function is intersecting twice and touching the x axis once in the path. So we will count that the function has only 3 distinct roots.