﻿ Function Rule Worksheet | Problems & Solutions Function Rule Worksheet

Function Rule Worksheet
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1.
Frank works as a sales person. He earns a salary of $425 and 4% commission on his monthly sales. Write a function rule that relates his total earnings to sales and find his earnings for the month, if his monthly sales are$4000. a. $600 b.$585 c. $575 d.$745

Solution:

Let, x be the amount of his sales

Let, f(x) be his total earnings, a function of his sales.

Total earnings = 425 + 4% of his monthly sales.
[In words.]

f(x) = 425 + 0.04(x)
[Substitute the value of his monthly sales.]

f(4000) = 425 + 0.04(4000)
[Replace x with 4000 to get his earnings in a month.]

= 425 + 160
[Multiply.]

= 585

Frank earns $585 for the month. Correct answer : (2) 2. A telephone company charges$24 as monthly rent and 70 cents per call. Write a function rule for the total monthly bill for a telephone connection. a. $f$($x$) = 24 + 0.7$x$ b. $f$($x$) = 24 + 70$x$ c. $f$($x$) = 24 + 7.0$x$ d. None of the above

Solution:

Let x be the number of calls made in a month.

Let f(x) be the total monthly bill.

Total monthly bill = $24 for monthly rent + (70 cents per call) x number of calls made [In words.] f(x) = 24 + 0.7(x) [Substitute the values.] The function rule for total monthly bill is f(x) = 24 + 0.7x. Correct answer : (1) 3. A library charges$0.7 per day for an overdue book. How much is charged for a book, which is 16 days overdue? a. $11.9 b.$12.6 c. $11.2 d.$10.5

Solution:

Let f(x) be the amount charged for a book, x days overdue.

The amount charged for the book x days overdue = 0.7x
[Write the variable expression.]

f(x) = 0.7x
[Write the function rule.]

f(16) = 0.7(16)
[Substitute 16 for x to find the amount for the book, 16 days overdue.]

= 11.2
[Multiply.]

So, the amount charged for the book, 16 days overdue is \$11.2.

4.
Write a rule to describe the number of pints of a liquid as a function of the number of quarts. a. f(x) = 0.5$x$ b. f(x) = 1.5$x$ c. f(x) = 4$x$ d. f(x) = 2$x$

Solution:

Let x be the number of quarts.

Let f(x) be the number of pints to x quarts.

x quarts is equivalent to 2x pints.
[1 quart = 2 pints.]

The function rule is f(x) = 2x.

5.
Write a function rule to describe the number of fluid ounces of a liquid as a function of the number of quarts. a. $f$($x$) = 32$x$ b. $f$($x$) = 16$x$ c. $f$($x$) = 0.03125$x$ d. None of the above

Solution:

Let x be the number of quarts.

Let f(x) be the number of fluid ounces to x quarts.

One quart is equivalent to 32 fluid ounces.

x quarts is equivalent to 32x ounces

So, the function rule is f(x) = 32x.

6.
Which of the following function rules describes the number of centimeters as function of the number of meters? a. $f$($x$) = 50$x$ b. $f$($x$) = 0.01$x$ c. $f$($x$) = 100$x$ d. None of the above

Solution:

Let x be the number of meters.

Let f(x) be the number of centimeters to x meters.

One meter is equivalent to 100 centimeters.

x meters is equivalent to 100x centimeters

So, the function rule is f(x)= 100x.

7.
Which of the following function rules describes the number of yards as function of number of miles? a. $f$($x$) = 240$x$ b. $f$($x$) = 1760$x$ c. $f$($x$) = 800$x$ d. None of the above

Solution:

Let x be the number of miles.

Let f(x) be the number of yards to x miles.

One mile is equivalent to 1760 yards.

x miles is equivalent to 1760x yards.

So, the function rule is f(x) = 1760x.

8.
Which of the following function rules describes the number of grams as function of number of kilograms? a. $f$($x$) = $\frac{x}{1000}$ b. $f$($x$) = 2640$x$ c. $f$($x$) = 1000$x$ d. None of the above

Solution:

Let x be the number of kilograms.

Let f(x) be the number of grams to x kilograms

One kilogram is equivalent to 1000 grams.

x kilograms is equivalent to 1000x grams
[words.]

f(x) = 1000x
[Rule.]

The function rule is f(x) = 1000x.

9.
Which of the following function rules describes the number of quarts as a function of number of gallons? a. $f$($x$) = $\frac{x}{4}$ b. $f$($x$) = 4$x$ c. $f$($x$) = 2$x$ d. None of the above

Solution:

Let x be the number of gallons.

Let f(x) be the function describing the number of quarts to x gallons.

One gallon is equivalent to 4 quarts.

x gallons is equivalent to 4x quarts.

The function rule is f(x) = 4x.

10.
Which of the following function rules describes the number of seconds as a function of number of hours? a. f(x) = 60$x$ b. f(x) = 3600$x$ c. f(x) = $\frac{x}{3600}$ d. f(x) = $\frac{x}{60}$

Solution:

Let x be the number of hours.

Let f(x) be the function describing the number of seconds to x hours.

One hour is equivalent to 3600 seconds.

x hours is equivalent to 3600x seconds.

So, the function rule is f(x) = 3600x.