Question

to rent a car from speedy rentals for one day, the cost varies as shown in the table.
which function rule best represents these data?
rental car costs
miles driven | rental cost
45 | $68.10
72 | $72.96
157 | $88.26
319 | $117.42
441 | $139.38
options:
$f(x) = ($0.18)x$
$f(x) = $60x$
$f(x) = ($5.56)x$
$f(x) = ($0.18)x + $60$

Explanation:

Step1: Check the first option

For \( f(x) = (\$0.18)x \), when \( x = 45 \), \( f(45)=0.18\times45 = 8.1\), which is not equal to \( 68.10 \). So this option is wrong.

Step2: Check the second option

For \( f(x)=\$60x \), when \( x = 45 \), \( f(45)=60\times45 = 2700\), which is not equal to \( 68.10 \). So this option is wrong.

Step3: Check the third option

For \( f(x)=(\$5.56)x \), when \( x = 45 \), \( f(45)=5.56\times45 = 250.2\), which is not equal to \( 68.10 \). So this option is wrong.

Step4: Check the fourth option

For \( f(x)=(\$0.18)x+\$60 \), when \( x = 45 \), \( f(45)=0.18\times45 + 60=8.1+60 = 68.1\), which matches the table value. Let's check another value, say \( x = 72 \), \( f(72)=0.18\times72+60 = 12.96 + 60=72.96\), which also matches. So this function rule best represents the data.

Answer:

\( f(x) = (\$0.18)x + \$60 \)