Q 41. - Precalculus Enhanced with Graphing Utilities

Question

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?

Step-by-Step Solution

Answer

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.

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

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. 

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.

Part (a) Step 4. Conclusion

Hence, graph

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

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.

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.

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).

Part (c) Step 2. Conclusion

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

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).

Part (d) Step 2. Conclusion

Hence, the graph

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

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.

Part (e) Step 2. Conclusion

Hence, the graph 

represent the swing situation.