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Chapter 2: Q. 68 (page 114)

In Problems 39-68, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y=x2) 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)=int(-x)

Short Answer

Expert verified

The graph of the function h(x)=int(-x)is:

Step by step solution

01

Step 1. Given

The functionh(x)=int(-x)

To graph the function and to find its domain and range.

02

Step 2. Graph the basic function

Graph the basic function h(x)=int(x)

03

Step 3. Replace int (x)by int (-x)

Replace h(x)=int(x)by

h(x)=int(-x)so that the graph is reflected about x-axis.

04

Step 4. Find domain and range

The domain and the range is the set of all real numbers.

05

Step 5. Verify the graph

Verify the graph by using graphing utility.

The graph of the function using graphing utility is:

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Most popular questions from this chapter

Cost of Trans-Atlantic Travel A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an airspeed of 500 miles per hour. The cost C (in dollars) per passenger is given by

C(x)=100+x10+36,000x

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(b) What is the cost per passenger with a head wind of 50 miles per hour?

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(d) What is the cost per passenger with a head wind of 100 miles per hour?

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-13+2

Suppose that the graph of a function f is known. Then the graph of y=f(x-2)may be obtained by a(n) ________ shift of the graph of f to the ________ a distance of2 units.

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.

The short-term

(no more than 24hours) parking fee F (in dollars) for

parking x hours at O鈥橦are International Airport鈥檚 main

parking garage can be modeled by the function

role="math" localid="1645828501222" F(x)=2if0<x鈮�14if1<x鈮�310if3<x鈮�45int(x+1)+2if4<x<951if9鈮�x鈮�24

Determine the fee for parking in the short-term parking

garage for

(a) 2hours

(b) 7hours

(c) 15hours

(d) 8hours and 24minutes
See all solutions

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