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)=

avissidep 2020-12-15 Answered
In the following items, you will analyze how several transformations affect the graph of the function f(x)=1x. Investigate the graphs of f(x)=1x,g(x)=f(x)=1x+2,h(x)=1x2,p(x)=1x4 and z(x)=1x2+1. 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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Expert Answer

Viktor Wiley
Answered 2020-12-16 Author has 84 answers

Step 1 We graph f(x), as well as g(x) (dotted line), h(x) (dashed line), and p(x) (solid line). image Step 2 We graph z(x): image Step 3 We find that the vertical asymptotes are f(x):x=0
g(x):x=2
h(x):x=2
p(x):x=4
z(x): 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).

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