Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each system of equations to its graph.
y = 2x + 1
y = x + 2
y = 3x
y = x + 3
y = 2x − 2
y = x − 2
y = 2x + 3
y = x + 5
y = 4x + 2
y = 3x + 2

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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.

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step-by-step explanation: