The graph below represents which of the following functions?

y=3sin2(x−

3

π

)

Step-by-step explanation:

The given function has a period of \piπ

The amplitude of the function 33 , because its range is -3\le y\le3−3≤y≤3

When the graph is shifted to the left by \frac{\pi}{3}

3

π

units, the function will be symmetric with respect to the origin.

Hence this graph is obtained by shifting the parent function with a period of \piπ , to the right by \frac{\pi}{3}

3

π

units.

this question relies purely on our observation of the graph and a knowledge of the behaviour of a graph of a hyperbola.

now, what we should realise is that there are two asymptotes - one at x = 0 and one at y = 0. what this means is that the graph will gradually approach, but never touch, these two lines. so, as x becomes more positive (ie. 'a very large positive number'), it will get closer to the line y = 0 (ie. the x-axis) - which means that the value of f(x) will gradually become smaller and closer to 0 - but will never reach it.

we can also observe this from the right half of the graph, where the graph gradually lowers closer and closer to the x-axis as x increases. what is important to note however is that it will never actually touch the x-axis (ie. f(x) will not equal 0) since there is an asymptote there. given this, we can see that option d, f(x) is a very small positive number, would be correct.