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Chapter 2: Q 42. (page 82)

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

(a) The temperature of a bowl of soup as a function of time.

(b) The number of hours of daylight per day over a 2-year period

(c) The population of Texas as a function of time.

(d) The distance traveled by a car going at a constant velocity as a function of time.

(e) The height of a golf ball hit with a 7-iron as a function of time.

Short Answer

Expert verified

Part (a) The graph (II) represent the situation temperature of a bowl of soup as a function of time.

Part (b) The graph (V) represent the situation number of hours of daylight per day over a 2-year period.

Part (c) The graph (IV) represent the population of Texas as a function of time.

Part (d) The graph (III) represent the situation distance traveled by a car going at a constant velocity as a function of time.

Part (e) The graph (I) represent the height of a golf ball hit with a 7-iron as a function of time.

Step by step solution

01

Part (a) Step 1. Given information.

We have given,

and

(a) The temperature of a bowl of soup as a function of time.

(b) The number of hours of daylight per day over a 2-year period.

(c) The population of Texas as a function of time.

(d) The distance traveled by a car going at a constant velocity as a function of time.

(e) The height of a golf ball hit with a 7-iron as a function of time.

02

Part (a) Step 2. Concept used.

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,

The temperature of a bowl of soup as a function of time.

Temperature of the bowl decreases time is increases.

This situation represent the graph (II).

04

Part (a) Step 4. Conclusion.

Hence, graph

represent the situation temperature of a bowl of soup as a function of time.

05

Part (b) Step 1. Explanation.

We have,

The number of hours of daylight per day over a 2-year period.

This is the swing situation and its represent the graph (V).

06

Part (b) Step 2. Conclusion.

Hence, the graph

Represent the situation number of hours of daylight per day over a 2-year period.

07

Part (c) Step 1. Explanation.

We have,

The population of Texas as a function of time.

When time increases the corresponding population of the Texas is also increases.

08

Part (c) Step 2. Conclusion.

Hence, the graph

Represent the situation population of Texas as a function of time.

09

Part (d) Step 1. Explanation.

We have,

The distance traveled by a car going at a constant velocity as a function of time.

When time increases the distance traveled by graph is also increases.

This situation represent the graph,

10

Part (d) Step 2. Conclusion.

Hence the graph

represent the situation distance traveled by a car going at a constant velocity as a function of time.

11

Part (e) Step 1. Explanation.

We have,

The height of a golf ball hit with a 7-iron as a function of time.

Height of the golf ball hit with a 7 iron is increases and then decreases.

This situation represent the graph

12

Part (e) Step 2. Conclusion.

Hence the graph

Represent the situation height of a golf ball hit with a 7-iron as a function of time.

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Most popular questions from this chapter

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.

An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure.

(a) Express the volume V of the box as a function of the length x of the side of the square cut from each corner.

(b) What is the volume if a 3-inch square is cut out?

(c) What is the volume if a 10-inch square is cut out?

(d) Graph V=V(x). For what value of x is V largest?

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.

The interval (2, 5) can be written as the inequality ___________

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.
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