Question

Assuming there are no reflections or dilations,

explain how you would write the oquation of the
function whose graph is sketched below.

Answer 1

Explanation:

We can see that this graph looks something like the graph of:

f(x) = 1/x^2

But the asymptotes of 1/x^2 are at x = 0, and in this case we can see that the asymptotes are near x = -3.

This may mean that the graph has been horizontally shifted 3 units to the left.

A general way to write an horizontal shift of N units is:

g(x) = f(x + N)

if N is positive, then the shift is to the left, if N is negative, then the shift is to the right.

In this case, we will have;

g(x) = f(x + 3)

And f(x) = 1/x^2

then:

g(x) = 1/(x + 3)^2

Graphing that, we get the graph shown below, that is almost the same as the graph in the image.