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Chapter 2: Q. 20 (page 209)

Match the two graphs shown here to the equations xy2+x=1andxy2+x+1=0Explain your choices.

Short Answer

Expert verified

The graph of the function:xy2+x=1:

Graph ofxy2+x+1=0

Step by step solution

01

Step 1. Given information:

The functions are:

xy2+x=11+x+xy2=0

02

Step 2. Find x-intercepts of both functions.

Substitute y=0in both functions and solve for x.

xy2+x=1x(1+y2)=1x(1+0)=1x=1

So x-intercept of this function is (1,0),

1+x+xy2=01+x+x.0=01+x=0x=-1

x-intercept is (-1,0)

03

Step 3. Match the graphs with their function.

Since xy2+x=1, has x-intercept is localid="1648443221959" (1,0),so the graph will cross at this point.

The localid="1648443300930" x-intercept of the function localid="1648443229137" 1+x+xy2=0is localid="1648443236418" (-1,0),so the graph will cross localid="1648443244527" x-axis at this point.

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