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Chapter 2: Q. 32 (page 69)

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

localid="1645890897117" y=±1-2x

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.

y=±1-2x

02

Step 2. The given equation is y=±1-2x

For values of x between -1 and 1, two values ofy result.

03

Step 3. For example, if x=0

y=±1-2×0y=±1

so two different outputs result from the same input. This means that the equation y=±1-2xdoes not define a function.

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Most popular questions from this chapter

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).

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

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.

g(x)=-x3

A rectangle has one corner in quadrant I on the graph of y=16-x2, another at the origin, a third on the positive y-axis and the fourth on the positive x-axis. See the figure.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Alargest?
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