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Graph Linear Functions Worksheet - Page 11

Graph Linear Functions Worksheet
  • Page 11
 101.  
Mr. Chris requires x gallons of milk for their family. The cost of x gallons of milk is given by f(x) = 1.19x. Which of the tables best suits the equation?

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


Solution:

f(x) = 1.19x
[Original equation.]

f(1)= 1.19(1) = 1.19
[Substitute 1 for x and simplify.]

f(2) = 1.19(2) = 2.38
[Substitute 2 for x and simplify.]

f(3) = 1.19(3) = 3.57
[Substitute 3 for x and simplify.]

f(4)= 1.19(4) = 4.76
[Substitute 4 for x and simplify.]

Table 3 matches with the equation.


Correct answer : (3)
 102.  
Find the slope and y-intercept of the function f(x) = 9.1 + 0.25x.
a.
Slope = 9.35, y-intercept = 0.50
b.
Slope = 0.25, y-intercept = 9.1
c.
Slope = 9.1, y-intercept = 0.25
d.
Slope = 0.50, y-intercept = 9.35


Solution:

f(x)= 0.25x + 9.1
[Original equation.]

f(x) = mx + c
[Standard equation.]

The slope of the function m is 0.25 and the y-intercept, c is 9.1.
[Compare with the standard equation.]


Correct answer : (2)
 103.  
If f(x) = 0.95x + 2.3, then find the value of f(2) and f(3).
a.
5.20, 6.65
b.
4.20, 5.15
c.
3.70, 5.65
d.
5.35, 7.30


Solution:

f(x) = 0.95x + 2.3
[Original equation.]

f(2) = 0.95(2) + 2.3
[Substitute 2 for x.]

= 4.20
[Simplify.]

f(3) = 0.95 (3) + 2.3
[Substitute 3 for x.]

= 5.15
[Simplify.]

So, f(2) = 4.20 and f(3) = 5.15


Correct answer : (2)
 104.  
Marissa and Jessica wanted to organize a farewell party for their seniors. They collected an amount of $800 from the class. The caterers charged $50 for each person. Which of the following functions shows the amount left with them?
a.
f(x) = 850 + 800x
b.
f(x) = 800 - 50x
c.
f(x) = 850 - 800x
d.
None of the above


Solution:

The total amount collected from the class = $800.

The amount charged by caterers per person = $50.

The balance depends on the number of people who attended the party = f(x) = 800 - 50x.

f(x) = 800 - 50x.
[Function rule.]


Correct answer : (2)
 105.  
Which of the input-output tables forms a linear function?

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


Solution:

A table is said to be a function if the ratio of change in input to output is same through out the table.

In the first table change in f(x)change in x is not same through out. So, it is ruled out.


[Consider table2.]

The change in input (x) is 3 and the change in output f(x) is 4.

Change in f(x)Change in x = 4 / 3

Among the choices, table 2 forms a linear function.
[The ratio of the change in f(x) to the change in x is same throughout the table.]


Correct answer : (2)
 106.  
Find the linear function for the graph.

a.
f(x) = (- 32)x + 10
b.
f(x) = (- 32)x +12
c.
f(x) = (- 32)x + 11
d.
None of the above


Solution:


Represent the data in the graph in a table, as shown below.

The change in input, x is + 2 and the change in output, f(x) is - 3.

Change in f(x)Change in x = -3 / 2

So, the slope of the function is - 32 .

The point (0, 10) lies on the graph of the function. So, the y - intercept is 10.

The function rule which governs the graph is f(x) = - 32x + 10
[Write the linear function as f(x) = mx + c.]


Correct answer : (1)
 107.  
Fuel is being pumped into a tanker at a rate of 75 gallons per minute. The quantity of fuel in the tanker is a function of the number of minutes the fuel is pumped. Which of the following equations represents the quantity of fuel in the tanker?
a.
A = 75 n
b.
A= 75 - n
c.
A= 75 + n
d.
A = 75n


Solution:

The rate at which fuel is being pumped is 75 gallons per minute.

Let n be the number of minutes, for which fuel is pumped and A be the amount of fuel in the tank.

The amount of fuel in the tank, A = 75 x number of minutes for which fuel is pumped

So, the equation representing the amount of fuel in the tanker is A = 75n


Correct answer : (4)
 108.  
A Painting exhibition is being organized in Milan. The painters who wish to exhibit and sell their paintings need to pay $100 for the space and $20 for each painting they sell. Which of the following equations best suits the function rule that represents the amount paid to the organizers as a function of number of paintings sold? Represent this as a function table showing input and output.
a.
f(x) = 100 + 20x
b.
f(x) = 100 + 30x
c.
f(x) = 120 + 20x
d.
None of the above


Solution:

Amount to be paid for space = $100.

Amount to be paid for each painting = $20.

Input(x) = Number of paintings each painter sells.

Output f(x) = Amount paid by each painter.


f(x) = 100 + 20x.


Correct answer : (1)
 109.  
A fete is being organized in a school. Students need to pay $50 to put up a games stall and $2 on every ticket they sell for the game. How much should each stall owner pay? Express this as a function rule.
a.
f (x) = 50 - 2x
b.
f (x) = 50 - x
c.
f(x) = 50 + 2x
d.
f (x) = 50 + x


Solution:

Let x be the number of tickets sold by the games stall owner.
[Input.]

Let f(x) be the amount earned by the stall owner.
[Output.]

f(x) = 50 + 2x
[Function rule.]


An input-output table is drawn, for the corresponding input values x = 4, 6, 8 and 10.


Correct answer : (3)
 110.  
Which of the following function rules best suits the graph?

a.
y = 4 + 2x
b.
y = 6 - 2x
c.
y = 7 + 3x
d.
y = - 5 + 3x


Solution:


Represent the data in the graph in a tabular form, as shown below.

The change in input (x) = 1

The change in output (y) = + 3

Change in yChange in x = + 31 = 3.

The slope of the line is 3 and y-intercept is - 5.
[Slope of the line is change in ychange in x.]

y = - 5 + 3x.
[Function rule.]


Correct answer : (4)

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