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 \(\displaystyle{f{{\left({x}\right)}}}:{x}={0}\)

\(\displaystyle{g{{\left({x}\right)}}}:{x}=-{2}\)

\(\displaystyle{h}{\left({x}\right)}:{x}={2}\)

\(\displaystyle{p}{\left({x}\right)}:{x}={4}\)

\(\displaystyle{z}{\left({x}\right)}:\) 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).