(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 $0.000.00 1 $1.301.30 2 $2.602.60 3 $3.903.90
Part 2
(b) The linear function that gives a rule for the amount charged is f(x)=
1.30 x.1.30x.
Part 3
(c) Choose the correct graph below.
A.
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A coordinate system has a horizontal x-axis labeled from negative 4 to 8 in increments of 1 and a vertical y-axis labeled from negative 2 to 8 in increments of 1. Points are plotted at (0, 0), (1.30, 0), (2.60, 0), and (3.90, 0).
B.
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A coordinate system has a horizontal x-axis labeled from negative 2 to 8 in increments of 1 and a vertical y-axis labeled from negative 4 to 8 in increments of 1. Points are plotted at (0, 0), (1, 1.30), (2, 2.60), and (3, 3.90).
C.
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A coordinate system has a horizontal x-axis labeled from negative 4 to 8 in increments of 1 and a vertical y-axis labeled from negative 2 to 8 in increments of 1. A plotted horizontal line lies along the x-axis.
D.
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The correct answer for part (c) is option B.
(a) Completed chart:
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.
(c) The correct graph is option B. A coordinate system has a horizontal x-axis labeled from -2 to 8 in increments of 1 and a vertical y-axis labeled from -4 to 8 in increments of 1. Points are plotted at (0, 0), (1, 1.30), (2, 2.60), and (3, 3.90).
To determine the price the taxicab driver charges for a trip of x miles, we can use the given rate of $1.30 per mile.
(a) We can calculate the price by multiplying the number of miles by the rate of $1.30.
Using the chart provided:
- For x = 0 miles, the price f(x) would be 0 * $1.30 = $0.00.
- For x = 1 mile, the price f(x) would be 1 * $1.30 = $1.30.
- For x = 2 miles, the price f(x) would be 2 * $1.30 = $2.60.
- For x = 3 miles, the price f(x) would be 3 * $1.30 = $3.90.
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 can be obtained by recognizing that the price (f(x)) is directly proportional to the number of miles (x), with a constant of proportionality being $1.30 per mile.
(c) To graph this linear function for the domain {0, 1, 2, 3}, we can plot the corresponding points and connect them with a straight line.
The correct graph is option B, which has points plotted at (0, 0), (1, 1.30), (2, 2.60), and (3, 3.90). The x-axis is labeled from -2 to 8 in increments of 1, and the y-axis is labeled from -4 to 8 in increments of 1.