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1.
What are the values of the function rule $f$ ($x$) = 6 $x$ - $x$2, for $x$ = 3, 4, 5 and 6?
 a. 9, 8, 5, 0 b. 8, 0, 9, 5 c. 9, 7, 0, 5 d. 3, 10, 8, 5

#### Solution:

f(x) = 6x - x2
[Original equation.]

f(3) = 6(3) - (3)2 = 18 - 9 = 9
[Substitute 3 for x and simplify.]

f(4) = 6(4) - (4)2 = 24 - 16 = 8
[Substitute 4 for x and simplify.]

f(5) = 6(5) - (5)2 = 30 - 25 = 5
[Substitute 5 for x and simplify.].]

f(6) = 6(6) - (6)2 = 36 - 36 = 0
[Substitute 6 for x and simplify.]

The value of the function rule f(x) = 6x - x2, for x = 3, 4, 5 and 6 is 9, 8, 5, 0, respectively.

2.
What are the values of the function rule $f$($x$) = 4$x$2 - 4, if $x$ = -4, -3, 2 and 3?
 a. 60, 32, 12, 32 b. 60, 32, 32, 12 c. 60, 12, 32, 32 d. 32, 60, 12, 32

#### Solution:

f(x) = 4x2 - 4
[Original equation.]

f(-4) = 4(-4)2 - 4 = 60
[Substitute -4 for x.]

f(-3) = 4(-3)2 - 4 = 32
[Substitute -3 for x.]

f(2) = 4(2)2 - 4 = 12
[Substitute 2 for x.]

f(3) = 4(3)2 - 4 = 32
[Substitute 3 for x.]

The value of f(x) = 4x2 - 4, for x = -4, -3, 2, 3 is 60, 32, 12, 32, respectively.

3.
In a biological research laboratory, the number of bacteria produced (output) is a function of the number of the experiments conducted (input). The function rule is f ($x$) = 0.2$x$2 - 0.6$x$. Which of the tables satisfies the given condition?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

f (x) = 0.2x2 - 0.6x.
[Original equation.]

f (20) = 0.2(20)2 - 0.6(20).
[Substitute 20 for x.]

= 68
[Simplify.]

f (40) = 0.2(40)2 - 0.6(40)
[Substitute 40 for x.]

= 296
[Simplify.]

f (60) = 0.2(60)2 - 0.6(60)
[Substitute 60 for x.]

= 684
[Simplify.]

f (80) = 0.2(80)2 - 0.6(80)
[Substitute 80 for x.]

= 1232
[Simplify.]

Table 2 represents the function rule.

4.
Which of the following rules satisfies the table?
 Input($x$) 4 5 6 7 Output $f$($x$) 21 30 41 54

 a. $f$($x$) = $x$2 + 4 b. $f$($x$) = $x$2 + 5 c. $f$($x$) = $x$2 - 4 d. None of the above

#### Solution:

f(x) = x2 + 4
[Consider choice A.]

f(4) = (4)2 + 4 = 20
[Substitute 4 for x.]

Since the first value in the table is 21, this rule is not valid.

f(x) = x2 + 5
[Consider choice B.]

f(4) = (4)2 +5
[Substitute 4 for x.]

= 21
[Simplify.]

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

= 30
[Simplify.]

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

= 41
[Simplify.]

f(7) = (7)2 + 5
[Substitute 7 for x.]

= 54
[Simplify.]

The rule that satisfies the table is f(x) = x2 + 5.

5.
What are the values of the function rule $f$($x$) = 3$x$2 - 3, for $x$ = - 3, 0, 3, 4?
 a. 24, -3, 24, 45 b. 24, -3, 25, 45 c. 24, -3, 24, 46 d. 25, -3, 24, 45

#### Solution:

f(x) = 3x2 - 3
[Original equation.]

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

= 24
[Simplify.]

f(0) = 3(0)2 - 3
[Substitute 0 for x.]

= -3
[Simplify.]

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

= 24
[Simplify.]

f(4) = 3(4)2 - 3
[Substitute 4 for x.]

= 45
[Simplify.]

The values of f(x) for the values of x are 24, -3, 24, 45, respectively.

6.
Which of the following rules represents the quadratic function?
 Input $x$ 1 2 3 4 Output $f$($x$) 2 -2 -12 -28

 a. $f$($x$) = 5$x$ - 3$x$2 b. $f$($x$) = $x$ - 3$x$2 c. $f$($x$) = 5$x$ - $x$2 d. None of these

#### Solution:

f(x) = 5x - 3x2
[Consider choice A.]

f(1) = (5 × 1) - (3 × 12) = 2
[Substitute 1 for x.]

f(2) = (5 × 2) - (3 × 22) = -2
[Substitute 2 for x.]

f(3) = (5 × 3) - (3 × 32) = -12
[Substitute 3 for x.]

f(4) = (5 × 4) - (3 × 42) = -28
[Substitute 4 for x.]

The rule that satisfies the quadratic function is f(x) = 5x - 3x2.

7.
Write a rule for the quadratic function.
 Input $x$ 0 1 2 3 Output $f$($x$) -3 -1 5 15

 a. $f$($x$) = 2$x$2 - 3 b. $f$($x$) = $x$2 - 3 c. $f$($x$) = 2$x$2 + 3 d. None of the above

#### Solution:

f(x) = 2x2 - 3
[Considering choice A.]

f(0) = (2 x 02) - 3 = -3
[Substitute 0 for x.]

f(1)= (2 x 12) - 3 = -1
[Substitute 1 for x.]

f(2) = (2 x 22) - 3 = 5
[Substitute 2 for x.]

f(3) = (2 x 32) - 3 = 15
[Substitute 3 for x.]

The rule that satisfies the quadratic function is f(x) = 2x2 - 3.

8.
What are the values of the function $f$($x$) = $x$2 - 3$x$ + 3, for v$x$ = - 4, - 3, 0, 3?
 a. 31, 21, 3 and 3 b. 31, 21, 3 and 6 c. 34, 21, 3 and 3 d. 31, 24, 3 and 3

#### Solution:

f(x) = x2 - 3x + 3
[Original equation.]

f(-4) = (-4)2 - 3(-4) + 3
[Substitute -4 for x.]

= 31
[Simplify.]

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

= 21
[Simplify.]

f(0) = (0)2 - 3(0) + 3
[Substitute 0 for x.]

= 3
[Simplify.]

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

= 3
[Simplify.]

The values of the function rule are 31, 21, 3 and 3.

9.
What are the values of the function rule $f$($x$) = 3$x$ + 2, for $x$ = 3, 5, 7, 9?
 a. 11, 22, 23, 29 b. 11, 17, 23, 29 c. 11, 17, 30, 29 d. 14, 17, 23, 29

#### Solution:

f(x) = 3x + 2
[Original equation.]

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

= 11
[Simplify.]

f(5) = 3(5) + 2
[Substitute 5 for x.]

= 17
[Simplify.]

f(7) = 3(7) + 2
[Substitute 7 for x.]

= 23
[Simplify.]

f(9) = 3(9) + 2
[Substitute 9 for x.]

= 29
[Simplify.]

The values of the function rule for the values of x are 11, 17, 23, 29, respectively.

10.
Gibson invests \$150 in a business and gets an interest of 10% compounded annually. The function $f$($x$) = 150(1.10)$x$ describes the amount after $x$ years. Which of the following quadratic functions represents the rule for 2, 5, 8, 10 years?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

f(x) = 150(1.10)x
[Original equation.]

f(x) = 150(1.10)2
[Substitute 2 for x.]

= 181.50
[Simplify.]

f(x) = 150(1.10)5
[Substitute 5 for x.]

= 241.57
[Simplify.]

f(x) = 150(1.10)8
[Substitute 8 for x.]

= 321.50
[Simplify.]

f(x) = 150(1.10)10
[Substitute 10 for x.]

= 389.06
[Simplify.]

Table-3 best suits for the function f(x) = 150(1.10)x.