Question

The function f(x) = 2-2+2+5 is graphed below. Plot all lattice points of the
inverse. Use the labeled points as your guide.
Click on the graph to plot a point. Click a point to delete it.
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Answer 1

Answer:

The inverse function and its corresponding lattice points are shown in blue on the attached graph.

The lattice points of the inverse are (9, 0), (7, 1) and (6, 2).

Step-by-step explanation:

Lattice points are coordinates in a two-dimensional grid system where both the x and y coordinates are integers, typically represented by intersections of horizontal and vertical gridlines.

The graph of the inverse of a function is the reflection of the original function in the line y = x. So, the inverse of a function essentially swaps the roles of x and y.

The lattice points of the original function are (0, 9), (1, 7) and (2, 6).

Therefore, the corresponding lattice points of the inverse are (9, 0), (7, 1) and (6, 2).

In the original function f(x), as x approaches infinity, the $2^{-x+2}$ part of the function approaches zero, indicating that f(x) approaches y = 5 but never quite reaches it. Consequently, there is a horizontal asymptote at y = 5 for the original function. As a result, the inverse function has is a vertical asymptote at x = 5.