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Chapter 4: Q. 7 (page 234)

In Problems 7-44, follow Steps 1through 7on page 228to analyze the graph of each function.

Rx=x+1xx+4

Short Answer

Expert verified

The graph for the function Rx=x+1xx+4is,

Step by step solution

01

Step 1 Given function is,

Rx=x+1xx+4

The domain of Ris, x|x鈮�0,-4.

As the value 0does not in the domain, there is no y-intercept.

The function Ris in the lowest terms.

The real zero of the numerator satisfies the equationx+1=0. So, thex- intercept is,-1.

02

Step 2 The real zeros of the denominator are the real solutions of the equation.

xx+4=0x=0,-4

The lines x=0,x=-4are the vertical asymptotes of the graph.

In the given function, the degree of the numerator is less than the degree of the denominator. So, Ris proper.

So, the line y=0is the horizontal asymptote of the graph.

Substitute Rx=0in the given equation.

x+1x(x+4)=0x+1=0x=-1

So, the graph intersects the horizontal asymptote at -1,0.

03

Step 3 Now plot a graph by using the known values.

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