When the graph of $y = f(x)$ is reflected in the line $y = x$, the number of invariant points is

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The graph of the function is given in the image

What are the invariants?

Would the invariant points be where the points of reflected graph and original intersect?

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The invariant points are going to be the points that do not change when a function undergoes one or more transformations. Invariant points will also occur on the graph of a function when they lie on the line of reflection. Therefore, there are two invariant points, one is at $(-1, -1)$ and the other is at $(1.5, 1.5)$. Both of the these lie on the line of reflection of $y = x$.