Use the graph of y fx below to answer parts ac Approximate

Use the graph of y = f(x) below to answer parts (a)-(c). Approximate, if necessary. (a) What is the domain and range of f(x)? (b) For what value(s) of x is f(x) > 0? (c) What are the real zeroes of f(x)? What is the multiplicity of each real zero (odd or even)?

Solution

a) Graph has a vertical asymtote at x = 3

So, Domain: ( -inf , 3) U ( 3, inf )

Range: In the -ve axis graph exists till y =-3 and exists upto infinity on the +ve side

( -3 , infinity)

b) for what values of x f(x) >0

( - inf , 3) U (10.5 , infinity )

c) Real zeros of f(x) ; x= 3.5 , x = 7.5 ( double multiplicity as graph touches the x axis)

                                  x = 10.5