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Chapter 2: Q 41. (page 79)

Match each of the following functions with the graph that best describes the situation.

(a) The cost of building a house as a function of its square footage.

(b) The height of an egg dropped from a 300-foot building as a function of time.

(c) The height of a human as a function of time.

(d) The demand for Big Macs as a function of price.

(e) The height of a child on a swing as a function of time?

Short Answer

Expert verified

Part (a) The graph (III) represent the graph of a function cost of building a house as a function of its square footage.

Part (b) The graph (IV) represent the graph of the function height of an egg dropped from a 300-foot building as a function of time.

Part (c) The graph (I) represent the graph of the function height of a human as a function of time.

Part (d) The graph (V) represent the graph of the function demand for Big Macs as a function of price

Part (e) The graph (II) represent the graph of the function height of a child on a swing as a function of time.

Step by step solution

01

Part (a) Step 1. Given information

We have given graphs are,

and the given functions are:

(a) The cost of building a house as a function of its square footage

(b) The height of an egg dropped from a 300-foot building as a function of time

(c) The height of a human as a function of time

(d) The demand for Big Macs as a function of price

(e) The height of a child on a swing as a function of time

02

Part (a) Step 2. Concept

A position- time graph:

A position- time graph shows how far an object has traveled from its starting position at any given time since it started moving.

03

Part (a) Step 3. Explanation

We have given function is,

The cost of building a house as a function of its square footage.

If measurement in square footage increases then the cost of building is also increase.

This situation represent the graph (III) because when x values increases corresponding y values are also increases.

04

Part (a) Step 4. Conclusion

Hence, graph

Represent the function cost of building a house as a function of its square footage.

05

Part (b) Step 1. Explanation

We have given,

The height of an egg dropped from a 300-foot building as a function of time.

When we drop graph from the building the initial height is 300 foot and its dropped down when we dropped egg to down it dropped on earth so when time increases height is decreases.

This situation represent the graph (IV) only.

06

Part (b) Step 2. Conclusion

Hence, the graph

represent the function height of an egg dropped from a 300-foot building as a function of time.

07

Part (c) Step 1. Explanation

We have given,

The height of a human as a function of time.

When time increases the height of the human increase but after some time humans height is constant.

This situation represent the graph (I).

08

Part (c) Step 2. Conclusion

Hence, the function height of a human as a function of time represent the graph (I)

09

Part (d) Step 1. Explanation

We have given,

The demand for Big Macs as a function of price.

When demand of Macs increases price is also increases.

This situation represent the graph (V).

10

Part (d) Step 2. Conclusion

Hence, the graph

Represent the demand for Big Macs as a function of price.

11

Part (e) Step 1. Explanation

We have given,

The height of a child on a swing as a function of time.

Here the graph (II) represent the swing situation.

12

Part (e) Step 2. Conclusion

Hence, the graph

represent the swing situation.

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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

Use the given graph of the function f to answer parts (a) 鈥� (n).

(a) Find f0 and f6.

(b) Find f2and f-2.

(c) Is f3positive or negative?

(d) Is f-1positive or negative?

(e) For what values of x is fx=0?

(f) For what values of x is localid="1650172833683" fx<0?

(g) What is the domain of f ?

(h) What is the range of f ?

(i) What are the x-intercepts?

(j) What is the y-intercept?

(k) How often does the line y = -1 intersect the graph?

(l) How often does the line x = 1 intersect the graph?

(m) For what value of x does fx=3?

(n) For what value of x does fx=-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.

Concepts and Vocabulary

True or False: A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 , we havef(x1)>f(x2)

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)
See all solutions

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