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Chapter 2: Q. 31 (page 69)

Determine whether the equation defines y as a function of x.

y2=4-x2

Short Answer

Expert verified

The given equation is not define a function.

Step by step solution

01

Step 1. Given information

In the given question we have to determine whether the equation defines y as a function of x.

y2=4-x2

02

Step 2. The given equation is y2=4-x2

To determine whether the given equation is a function, solve the equation fory.

03

Step 3. Solving the equation for y.

Taking square root on both side

y2=4-x2y=卤4-x2
04

Step 4. For values of x between -4 and 4, two values of y result.

For example, ifx=1

y=卤4-x2y=卤4-(1)2y=卤4-1y=卤3
05

Step 5. When we put x=1 in the equation then we found y=±3

So two different outputs result from the same input. This means that the equation y2=4-x2does not define a function.

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Most popular questions from this chapter

In Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the right4 units

Determine whether each relation represents a function. For each function, state the domain and range.

-1,0,2,3,4,0

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

h(x)=x-2

A wire of length xis bent into the shape of a circle.

Part (a): Express the circumference Cof the circle as a function of x.

Part (b): Express the areaAof the circle as a function ofx.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=-x
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