# In the following items, you will analyze how several transformations affect the graph of the function f(x)=frac{1}{x}. Investigate the graphs of f(x)=

In the following items, you will analyze how several transformations affect the graph of the function $f\left(x\right)=\frac{1}{x}$. Investigate the graphs of . If you use a graphing calculator, select a viewing window $±23.5$ for x and $±15.5$ for y. At what values in the domain did vertical asymptotes occur for each of the functions? Explain why the vertical asymptotes occur at these values.
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Step 1 We graph f(x), as well as g(x) (dotted line), h(x) (dashed line), and p(x) (solid line). Step 2 We graph z(x): Step 3 We find that the vertical asymptotes are $f\left(x\right):x=0$
$g\left(x\right):x=-2$
$h\left(x\right):x=2$
$p\left(x\right):x=4$
$z\left(x\right):$ None Each vertical asymptote is found by finding the value(s) of x for which the denominator equals zero, and therefore the function is undefined. Note that there is no such real value of x in the case of z(x).