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# Function Worksheet

Function Worksheet
• Page 1
1.
Which of the following equations best represents the table?

 a. $y$ = 5$x$ - 4 b. $y$ = $x$ - 1 c. $y$ = 2$x$ - 1 d. $y$ = 2$x$ + 2

#### Solution:

The values of y obtained when x = 1, 2, 3, 4, 5 in y = 2x + 2 are 4, 6, 8, 10, 12.

The values of y obtained when x = 1, 2, 3, 4, 5 in y = 5x - 4 are 1, 6, 11, 16, 21.

The values of y obtained when x = 1, 2, 3, 4, 5 in y = x - 1 are 0, 1, 2, 3, 4.

The values of y obtained when x = 1, 2, 3, 4, 5 in y = 2x - 1 are 1, 3, 5, 7, 9.

The values of y obtained for the equation y = 2x - 1 are same as that of the values given in the table.

So, the equation y = 2x - 1 best represents the given table.

Correct answer : (3)
2.
Andrew deposited $10 initially in his bank account. Then he deposited$5 every week. The total savings, '$c$' is represented by the equation, $c$ = 10 + 5$n$, where '$n$' denotes the number of weeks. Which table of values satisfies the equation?

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

#### Solution:

Substitute from 0 to 5 for 'n' in the equation.

You get the following table of values.

Compare the labels and values in this table with the tables given in the question.

So, values in table 1 satisfies the given equation.

Correct answer : (4)
3.
Which of the following equations is not a linear equation?
 a. 3$x$ + $y$ - 5 = - 7$x$ + 4$y$ + 3 b. 3$x$ = 10 c. 3$a$ + 472$b$ = 10$b$ + 37 d. $x$2 - 1 = 15

#### Solution:

An algebraic equation is said to be linear if the variable or variables in the equation are of first degree.

In the equation x2 - 1 = 15, x is raised to the power 2.

So, x2 - 1 = 15 is not a linear equation.

Correct answer : (4)
4.
Identify the graph that represents a linear function.

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

#### Solution:

The graph of a linear equation is a straight line.

Graph 2 is a straight line.

So, Graph 2 represents a linear equation.

Correct answer : (4)
5.
Identify the table that represents a linear function.

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

#### Solution:

The values in the Table 1 satisfy the function f(x) = x + 4

The values in the Table 2 satisfy the function f(x) = x2

The values in the Table 3 satisfy the function f(x) = 2x2

The values in the Table 4 satisfy the function f(x) = x2 - 1

The data in table 1 represents a linear function.

Correct answer : (1)
6.
The length ($l$) and the width ($w$) of a rectangle with an area of 48 m2 are related by the equation $l$$w$ = 48. Which of the following best describes the model?
 a. can′t be determined b. indirect variation c. direct and indirect variation d. direct variation

#### Solution:

For a constant area of a rectangle, the length (l) and the width (w) vary inversely.

Therefore, equation lw = 48 describes an indirect variation.

Correct answer : (2)
7.
The perimeter ($P$) of a regular hexagon is 6 times the length of a side ($s$). Which of the equations best relates the variables?
 a. $P$ = $\frac{s}{6}$ b. $P$ = 6$s$ c. $P$ = $\frac{6}{s}$ d. $s$ = 6$P$

#### Solution:

Perimeter (P) of the hexagon varies directly with length of a side (s).

Therefore, P = 6s is the equation that best relates the variables.

Correct answer : (2)
8.
A can of French onion soup weighs 325 grams. The weight of a box of $n$ cans of the soup is $W$. Which of the following equations best relates the variables?
 a. $W$ = $\frac{325}{n}$ b. $W$$n$ = 325 c. $W$ = $\frac{n}{325}$ d. $W$ = 325($n$)

#### Solution:

As the number of cans increase, the total weight of the box also increases.

Therefore, W = 325(n) best relates the variables.

Correct answer : (4)
9.
John earns $13 for every half an hour he works. Which of the graphs best represents the situation?  a. Graph 2 b. Graph 1 c. Graph 4 d. Graph 3 #### Solution: Let x be the number of hours John works. Amount of money John earns in one hour =$26

If John works for more hours, the amount of money he earns, increases.

Therefore, the direct variation between the number of hours John works and the amount of money he earns can be given as, amount of money John earns = 26 × x.

The number of hours John works and the amount he earns is given in the table.

Graph 3 best represents the situation.

Correct answer : (4)
10.
One pound of steak costs \$7.65. The total cost of $p$ pounds is $C$. Which of the equations best relates the variables?
 a. $C$$p$ = 7.65 b. $C$ = $\frac{7.65}{p}$ c. $C$ = 7.65 × $p$ d. $C$ = $\frac{p}{7.65}$

#### Solution:

As the number of pounds of steak increases, the total cost increases.

Therefore, C = 7.65 × p best relates the variables.

Correct answer : (3)

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