Concept explainers
To Graph:
Draw a graph to represent the cost of going over the mileage.
Explanation of Solution
Given Information:
As per Marcus’ leasing agreement , he will be charged $0.20 per mile for each mile over 12,000.Any fraction of a mile is rounded up to the next mile.
Concept Used:
Least Integer Function:
The function whose value at any number x is the smallest integer greater than of equal to x is called the least integer function.
It is denoted by
For example
Calculation:
Charges per mile above 12,000 miles = $0.20
For any fraction of a mile above 12,000 miles , we round it up to the next mile and then take the following steps ( for example , for 0.6 miles , we take number of miles , x = 1) :
So , for x miles above 12,000 miles , we take ceiling of x =
So, for x miles above 12,000 miles, we have the charges will be applied =
Cost of going x miles above 12,000 miles =
We make a table for different number of miles above 12,000 miles and Cost of going above the mileage:
Number of miles over 12,000 (x) | Rounded up value = | |
1 | 1 | 0.20 |
1.5 | 2 | 0.40 |
2 | 2 | 0.40 |
2.5 | 3 | 0.60 |
3 | 3 | 0.60 |
3.5 | 4 | 0.80 |
4 | 4 | 0.80 |
Graph:
From the table above , we draw the graph of the function :
Where to use the dots and circles :
At 12,000 miles, the cost is included in rental, so it is a circle at (0,0.20).
From 12,000 miles (excluded ) to 12,001 miles (included) , there is a cost of $0.20.
So, at x = 1( that is at 12,001 miles) , the cost is $0.20.
So, at (0,0.20) , there is a circle and at (1,0.20) , there is dot.
From 12,001 ( x =1) to 12,002 ( x = 2 ) miles , the cost is $0.40 , but 12,001 not included and 12,002 is included.
So, at (1,0.40) , there is a circle and at (2,0.40) , there is dot.
Plot the points and join.Continue the proess.
Chapter 4 Solutions
Algebra 1
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