Function Worksheets - Page 9

Function Worksheets
• Page 9
81.
Which of the tables satisfies the equation $m$ = 30 - 2$n$?

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

Solution:

m = 30 - 2n
[Original equation.]

To know which table satisfies the equation, substitute the input values given in the tables for n and check the results with the output values in the tables.

m = 30 - 2(2) = 26
[Substitute 2 for n.]

m = 30 - 2(9) = 12
[Substitute 9 for n.]

m = 30 - 2(11) = 8
[Substitute 11 for n.]

m = 30 - 2(15) = 0
[Substitute 15 for n.]

The output values for the corresponding input values 2, 9, 11 and 15 are 26, 12, 8 and 0.

Table-2 satisfies the equation.

82.
Which of the following choices represents a function?
 a. Input: Number of channels in your television; Output: Cost of the television b. Input: Number of fishes in an aquarium; Output: Cost of the aquarium c. Input: Time taken by the car to travel certain distance; Output: Distance traveled by the car d. None of the above

Solution:

A function represents the relation between the Input and the Output.

In the choices there is no relation between the Input and the Output except for choice C, since it shows the relation between the time and the distance.

83.
Joe and Andy were flying in a hot-air balloon for the first time. After they reached an altitude of 300 feet, they turned on the burner and then the balloon started rising to a height of 15 feet per 5 minutes. Which of the table satisfies the relation between input and output $h$ = 300 + 15$t$, where $t$ ≥ 0 and $t$ ≤ 4?

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

Solution:

h = 300 +15t
[Original equation.]

h = 300 + 15(0)
[Substitute 0 for t.]

h = 300
[Simplify.]

h = 300 + 15(1)
[Substitute 1 for t.]

= 315
[Simplify.]

h = 300 + 15(2)
[Substitute 2 for t.]

= 330
[Simplify.]

h = 300 +15(3)
[Substitute 3 for t.]

= 345
[Simplify.]

The input and output values of table-2 matches with the results of the equation.

So, table 2 satisfies the equation h = 300 + 15t.

84.
Which of the tables best suits the equation?
$y$ = 3(4$x$ + 12) [Use $x$ = 0 to 5]

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

Solution:

y = 3(4x + 12)
[Original equation.]

y = 3(4(0) +12) = 36
[Substitute 0 for x.]

y = 3(4(1) + 12) = 48
[Substitute 1 for x.]

y = 3(4(2) +12) = 60
[Substitute 2 for x.]

y = 3(4(3) +12) = 72
[Substitute 3 for x.]

y = 3(4(4) + 12) = 84
[Substitute 4 for x.]

y = 3(4(5) +12) = 96
[Substitute 5 for x.]

For the values of x, the corresponding values of y are 36, 48, 60, 72, 84 and 96.

So, table 4 best suits the equation y = 3(4x + 12)

85.
Write the equation that satisfies the input - output table.
 Input($x$) 0 1 2 3 4 5 Output($y$) 50 45 40 35 30 25

 a. $y$ =50 - 6$x$ b. $y$ =50 - 5$x$ c. $y$ =50 - 7$x$ d. $y$ =50 - 8$x$

Solution:

y = 50 - 6x
[Consider choice A.]

50 - 6(0) = 50
[Substitute 0 for x.]

y = 50 - 6(1) = 44
[Substitute 1 for x.]

In the table for x = 1, y = 45. So first equation is ruled out.

y = 50 - 5x
[Consider choice B.]

y = 50 - 5(0) = 50
[Substitute 0 for x.]

y = 50 - 5(1) = 45
[Substitute1 for x.]

y = 50 - 5(2) = 40
[Substitute 2 for x.]

y = 50 - 5(3) = 35
[Substitute 3 for x.]

y = 50 - 5(4) = 30
[Substitute 4 for x.]

y = 50 - 5(5) = 25
[Substitute 5 for x.]

The equation y = 50 - 5x satisfies the table.

86.
Which of the graphs satisfies the input - output table?
 Input($x$) 0 1 2 3 4 5 Output($y$) 4 36 32 28 24 20

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

Solution:

From the table, as x is increases y increases up to x = 1 and then as x increases y decreases from x = 1 to x = 5.

Graph 3 satisfies the table.

87.
What is the value of $p$ for the function $p$ = 2$m$ + 4, if $m$ = 5?
 a. 16 b. 22 c. 14 d. 20

Solution:

p = 2m + 4
[Original equation.]

p = 2(5) + 4
[Substitute 5 for m.]

p = 14
[Simplify.]

The value of p is 14.

88.
A function $y$ = 8$x$ gives the equation of a line passing through the origin. If $x$ ≥ 0 and $x$ ≤ 5, then which table shows the relation between input and output for the function?

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

Solution:

As, x ≥ 0 and x ≤ 5, x takes the values between 0 and 5 including 0 and 5.

y = 8x
[Original equation.]

y = 8(0) = 0
[Substitute 0 for x.]

y = 8(1) = 8
[Substitute 1 for x.]

y = 8(2) = 16
[Substitute 2 for x.]

y = 8(3) = 24
[Substitute 3 for x.]

y = 8(4) = 32
[Substitute 4 for x.]

y = 8(5) = 40
[Substitute 5 for x.]

The values of y for the corresponding values of x are 0, 8, 16, 24, 32, and 40.

Table 1 satisfies the equation.

89.
Construct an input - output table for the equation $h$ = 120 + 15$t$, for 0 ≤ $t$ ≤ 4, and choose the graph that represents the equation correctly.

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

Solution:

h = 120 + 15t
[Original equation.]

As 0 ≤ t ≤ 4, substitute the values 0, 1, 2, 3, and 4 for t in the equation.

h = 120 + 15(0)
Substitute 0 for t in the equation.

h = 120
[Simplify.]

h = 120 + 15(1)
Substitute 1 for t in the equation.

= 135
[Simplify.]

h = 120 + 15(2)
Substitute 2 for t in the equation.

= 150
[Simplify.]

h = 120 + 15(3)
Substitute 3 for t in the equation.

= 165
[Simplify.]

h = 120 + 15(4)
Substitute 4 for t in the equation.

= 180
[Simplify.]

The values in the input-output table match with the points plotted in Graph 2.

So, Graph 2 represents the equation.