﻿ Function Worksheets - Page 10 | Problems & Solutions
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Function Worksheets
• Page 10
91.
The function $f$($x$) = 64$x$ describes the distance traveled by a car in miles and $x$ represents the time taken by the car. What is the distance traveled by the car in 3 hours? a. 196 b. 194 c. 200 d. 192

#### Solution:

f(x) = 64x
[Original equation.]

f(3) = 64 x 3
[Substitute 3 for x.]

= 192
[Simplify.]

The distance traveled by the car in 3 hours is 192 miles.

Correct answer : (4)
92.
What is the value of the function $f$(3), if $f$($x$) = 3$x$ + 9? a. 23 b. 24 c. 18 d. 26

#### Solution:

f(x) = 3x + 9
[Original equation.]

f(3) = 3(3) + 9
[Substitute 3 for x.]

= 18
[Simplify.]

Correct answer : (3)
93.
What is the value of the function $f$(6), if $f$($x$) = 5$x$ - 2? a. 30 b. 28 c. 32 d. 29

#### Solution:

f(x) = 5x - 2
[Original equation.]

f(6) = 5(6) - 2
[Substitute 6 for x.]

= 28
[Simplify.]

Correct answer : (2)
94.
Kelsey bought apples at $2 each. Write a function to represent the relation between the number of apples she bought $a$, and the total cost, $f$($a$). a. $f$($a$) =$a$/2 b. $f$($a$) = 2/$a$ c. $f$($a$) = 2$a$ d. None of the above #### Solution: The total cost = the cost of each apple x the number of apples she bought. f(a) =$2 x a
[Substitute the values.]

f(a) = 2a
[Simplify.]

The function that represents a relation between the number of apples and the total cost is f(a) = 2a.

Correct answer : (3)
95.
What are the values of $f$(-4), $f$(2) and $f$(3.2), if $f$($x$) = 9$x$2 - 2? a. 142, 34, 90.16 b. 147, 39, 95.16 c. 152, 44, 100.16 d. 146, 38, 94.16

#### Solution:

f(x) = 9x2 - 2
[Original equation.]

= 142
f(-4) = 9(-4)2 - 2
[Substitute -4 for x and simplify.]

= 34
f(2) = 9(2)2 - 2
[Substitute 2 for x and simplify.]

= 90.16
f(3.2) = 9(3.2)2 - 2
[Substitute 3.2 for x and simplify.]

Correct answer : (1)
96.
Evaluate $f$($x$) = 14 - 2$x$, for $x$ = 1, 2, 3, 4, and find the common difference for the output. a. 1 b. 3 c. 2 d. None of the above

#### Solution:

f(x) = 14 - 2x
[Original equation.]

f(1) = 14 - 2(1)
[Substitute 1 for x.]

= 12
[Simplify.]

f(2) = 14 - 2(2)
[Substitute 2 for x.]

= 10
[Simplify.]

f(3) = 14 - 2(3)
[Substitute 3 for x.]

= 8
[Simplify.]

f(4) = 14 - 2(4)
[Substitute 4 for x.]

= 6
[Simplify.]

f(1) = 12, f(2) = 10, f(3) = 8 and f(4) = 6.

The relation between the input and the output is as input is increased by 1 output is decreased by 2.

So, the common difference is 2.

Correct answer : (3)
97.
Laura had $7 with her. She sold $n$ cards at$3 each and earned some money. Identify an equation for the money she had with her finally. a. $f$($n$) = 7 - $n$ b. f($n$) = 7$n$ c. f($n$) = 3$n$ + 7 d. $f$($n$) = 3$n$ - 7

#### Solution:

The money she had finally = money earned by selling n cards + money she had initially

The money earned by selling n cards = n × cost of each card = n × 3 = \$3n

Let f(n) be the amount of money she had finally.

So, the equation for the total money she had finally is f(n) = 3n + 7

Correct answer : (3)
98.
Find the value of $f$(1), $f$(2), $f$(3) and $f$(4), if f($x$) = 4 × 0.1$x$. a. 4, 0.4, 0.04, and 0.004 b. 0.4, 0.004, 0.004, and 0.0004 c. 4, 0.04, 0.004, and 0.0004 d. 0.4, 0.04, 0.004, and 0.0004

#### Solution:

f(x) = 4 x 0.1x
[Original equation.]

f(1) = 4 x 0.11
[Substitute 1 for x.]

= 0.4
[Simplify.]

f(2) = 4 x 0.12
[Substitute 2 in place of x.]

= 0.04
[Simplify.]

f(3) = 4 x 0.13
[Substitute 3 in place of x.]

= 0.004
[Simplify.]

f(4) = 4 x 0.14
[Substitute 4 in place of x.]

= 0.0004
[Simplify.]

The values of f(1), f(2), f(3) and f(4) are 0.4, 0.04, 0.004 and 0.0004

Correct answer : (4)
99.
What are the values of $f$(- 4) and $f$(4), if $f$($x$) = $x$2? a. 16, 16 b. -16, -16 c. 16, -16 d. -16, 16

#### Solution:

f(x) = x2
[Original equation.]

f(4) = 42
[Substitute 4 for x.]

= 16
[Simplify.]

f(-4) = (-4)2
[Substitute -4 for x.]

= 16
[Simplify.]

Correct answer : (1)
100.
The function $f$($x$) = 80$x$ describes the distance traveled by a truck in miles and $x$ represents the time taken by the truck. What is the distance traveled by the truck in 7 hours? a. 474 b. 553 c. 560 d. 567

#### Solution:

f(x) = 80x
[original equation.]

f(7) = 80 x 7
[substitute 7 for x.]

= 560
[simplify.]

The distance traveled by the truck in 7 hours is 560 miles.

Correct answer : (3)

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