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Chapter 2: Q. 19 (page 210)

Match the two graphs shown here to the equations x+1y2+y-1=1and xy2+y=1Explain your choices.

Short Answer

Expert verified

The graph of x+1y2+y-1=1

The graph of xy2+y=1

Step by step solution

01

Step 1. Given information

The functions are:

First function: x+1y2+y-1=1

Second function: xy2+y=1

The graph;

02

Step 2. Find x-intercepts of both functions. 

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

x+1y2+y-1=10+1(y2+y-1)=1y2+y-1=1y2+y-2=0y2+2y-y-2=0y(y+2)-1(y+2)=0(y-1)(y+2)=0y-1=0y=1y+2=0y=-2

So y-intercepts of the first function are:0,-2and 0,1.

Similarly in second function:

0.y2+y+1=0y=-1

So y-intercept of the second function is0,-1

03

Step 3. Match the graphs with their function. 

Since x+1y2+y-1=1, has y-intercept are (0,-2)and (0,1),so the graph will cross at these points.

So the graph is:

The localid="1648474453130" y-intercept of localid="1648474461083" xy2+y=1is localid="1648474468644" 0,1

So the graph of the function crossesy-axis at this point.

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