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Chapter 2: Q. 29 (page 69)

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

y=1x

Short Answer

Expert verified

The given equation is 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.

y=1x

02

Step 2. The given equation is y=1x

The equation tells us to take an input xand find their square.

For any input x, these operations yield only one output y.

03

Step 3. For example, 

If x=1, then role="math" localid="1645888562472" y=11=1,x鈮�0.

If x=2, then role="math" localid="1645888640793" y=12,x鈮�0.

For this reason, the equation is a function.

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Find the following for each function:

fx=3xx2-1

Part (a):f2

Part (b):f-2

Part (c):f-x

Part (d):-fx

Part (e):fx-2

Part (f):f2x

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

In March 2011, Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge -\(13.55

Distribution charge

First 20therms-0.1473/therm

Next 30therm -\)0.0579/therm

Over 50therm -\(0.0519/therm

Gas supply charge-\)0.51/therm

(a) What is the charge for using 40therms in a month?

(b) What is the charge for using 150therms in a month?

(c) Develop a model that gives the monthly charge Cfor x therms of gas.

(d) Graph the function found in part (c).
See all solutions

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