Question

In the graph given below,
How many maximum values does $y$ can have for one value of $x$?

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is C $8$

In order to find out the number of values of $y$ for one value of $x$, we will use VLT (Vertical Line Test) in the above graph.
we will draw different vertical lines at different positions of curve and then check which line is intersecting at maximum points with the curve. Let us see by graph,
Here, we see that when line $l_1$ is drawn vertical to the curve, there are only $2$ points where it cuts the curve.
Now, when we draw the line $l_2$ vertical to the curve, it intersect the curve at $8$ different points.

And when lines $l_3$ and $l_4$ are drawn, we see that there are $6$ and $4$ points respectively where these lines cut the given curve.

Hence from the graph, we can say that there are maximum $8$ values of $y$ for a single value of $x$.
So, option $\left(c\right)$ is correct.