(a) Suppose that a taxicab driver charges $1.30 per mile. Fill in the chart shown to the right with the correct response for the price f(x) she charges for a trip of x miles.
(b) The linear function that gives a rule for the amount charged is f(x)=____.
(c) Graph this function for the domain {0, 1, 2, 3}.
x
f(x)
0
$__
1
$__
2
$__
3
$__
Question content area bottom
Part 1
(a) Complete the chart below.
x f(x) 0 $enter your response here 1 $enter your response here 2 $enter your response here 3 $enter your response here
x f(x)
0 $0.00
1 $1.30
2 $2.60
3 $3.90
(a) The price f(x) charged for a trip of x miles is as follows:
x f(x)
0 $0.00 (There is no charge for a trip of 0 miles.)
1 $1.30
2 $2.60
3 $3.90
To fill in the chart, we can use the given information that the taxicab driver charges $1.30 per mile.
(a) The price, f(x), the driver charges for a trip of x miles can be calculated by multiplying the number of miles by the price per mile. So, for x = 0 miles, the price would be $0. For x = 1 mile, the price would be $1.30. For x = 2 miles, the price would be $2.60. For x = 3 miles, the price would be $3.90.
So, the completed chart would be:
x f(x)
0 $0.00
1 $1.30
2 $2.60
3 $3.90
(b) The linear function that gives a rule for the amount charged is f(x) = 1.30x. This is because the price charged is directly proportional to the number of miles.
(c) To graph this function for the domain {0, 1, 2, 3}, we plot the points (0, 0.00), (1, 1.30), (2, 2.60), and (3, 3.90) on a graph. We can use the x-axis to represent the number of miles and the y-axis to represent the price in dollars. Then, we can connect the plotted points with a straight line to represent the linear function.