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Chapter 2: Q. 39 (page 113)

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)=x2-1

Short Answer

Expert verified

The graph of the function f(x)=x2-1is given as:

The domain of the function is (-鈭�,鈭�)and the range is[-1,鈭�)

Step by step solution

01

Step 1. given data

The given function isf(x)=x2-1

02

Step 2. Graph the parent function. 

The parent function of the given function isg(x)=x2

Plot the graph of the functiong(x)=x2

03

Step 3. Graph of the function 

Graph of function f(x)=x2-1can be obtained by shifting the graph of the functiong(x)=x2towards down by one unit.

The graph of the function is given as:

04

Step 4.  domain and range of the function

From the graph, we infer that

The domain of the function is(-鈭�,鈭�)

The range of the function isrole="math" localid="1645820040825" [-1,鈭�)

05

Step 5. Verification

plot the graph of the functionf(x)=x2-1 using a graphing utility

The graph is the same as we have drawn. Hence, it is correct.

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Most popular questions from this chapter

Wind Chill The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is

W={t0鈮�v<1.7933-(10.45+10v-v)(33-t)22.04,1.79鈮�v鈮�2033-1.5958(33-t),v>20

where vrepresents the wind speed (in meters per second) and trepresents the air temperature . Compute the wind chill for the following:

(a) An air temperature of localid="1645962228946" 10掳Cand a wind speed of 1 meter per second localid="1645962235368" (m/sec)

(b) An air temperature of localid="1645962241584" 10掳Cand a wind speed of localid="1645962248218" 5m/sec

(c) An air temperature of localid="1645962254138" 10掳Cand a wind speed of localid="1645962259043" 15m/sec

(d) An air temperature of localid="1645962265610" 10掳Cand a wind speed of localid="1645962274629" 25m/sec

(e) Explain the physical meaning of the equation corresponding to localid="1645962280348" 0鈮�v<1.79

(f) Explain the physical meaning of the equation corresponding to localid="1645962285160" v>20.

Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the origin.

In Problems 31鈥�36, graph each function using the techniques of shifting, compressing or stretching, and reflections. Identify any intercepts on the graph. State the domain and, based on the graph, find the range.

h(x)=(x-1)2+2

Motion of a Golf Ball A golf ball is hit with an initial velocity of 130 feet per second at an inclination of 45掳 to the horizontal. In physics, it is established that the height h of the golf ball is given by the function

h(x)=-32x21302+x

where x is the horizontal distance that the golf ball has traveled.

(a) Determine the height of the golf ball after it has traveled 100 feet.

(b) What is the height after it has traveled 300 feet?

(c) What is h(500)? Interpret this value.

(d) How far was the golf ball hit?

(e) Use a graphing utility to graph the function h = h(x).

(f) Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 90 feet.

(g) Create a TABLE with TblStart = 0 and 鈭�Tbl= 25. To the nearest 25 feet, how far does the ball travel before it reaches a maximum height? What is the maximum height?

(h) Adjust the value of 鈭�Tbluntil you determine the distance, to within 1 foot, that the ball travels before it reaches a maximum height.

Metro Media Cable is asked to provide service to a customer whose house is located 2 miles from the road along which the cable is buried. The nearest connection box for the cable is located 5miles down the road. See the figure.

(a) If the installation cost is \(500 per mile along the road and \)700 per mile off the road, build a model that expresses the total cost C of installation as a function of the distance x (in miles) from the connection box to the point where the cable installation turns off the road. Give the domain.

(b) Compute the cost if x=1mile.

(c) Compute the cost if x=3miles.

(d) Graph the function C=C(x). Use TRACE to see how the cost C varies as x changes from 0 to 5.

(e) What value of x results in the least cost?
See all solutions

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