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)=

Question

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) = \frac{1}{x}, g (x) = f (x) = \frac{1}{x + 2}, h (x) = \frac{1}{x - 2}, p (x) = \frac{1}{x - 4} and z (x) = \frac{1}{x^{2} + 1}

. If you use a graphing calculator, select a viewing window

\pm 23.5

for x and

\pm 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.

Answer 1

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 $f (x) : x = 0$
$g (x) : x = - 2$
$h (x) : x = 2$
$p (x) : x = 4$
$z (x) :$ 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).

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)=

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