Question

graph : 1/2(x-2)2

Answer 1

Question. Draw the graph of the function

$$f(x) = \frac{1}{2(x - 2)^2}.$$

Solution. First draw a graph of the function

$$f_1(x) = \frac{1}{2x^2}$$

Its domain is $(-\infty, 0) \cup (0, +\infty)$ and the lines $x = 0$ and $y = 0$ are asymptotes.

The graph looks like hyperbola with both branches above $x$-axis. It can be constructed by calculating some points of this graph

So the graphs will look as follows:

Now the graph of

$$f(x) = \frac{1}{2(x - 2)^2}$$

can be obtained from the graph of $f_1$ by moving it by 2 to the right:

It has assymptote $x = 2$ and $y = 0$ .