Function Worksheets - Page 2

Function Worksheets
• Page 2
11.
Nina and Katie wanted to organize a farewell party for their seniors. They collected an amount of $720 from the class. The caterers charged at the rate of$48 per person attended. Choose an equation to represent the situation assuming $x$ as the number of persons attended and $y$ as the amount left with Nina and Katie after the party.
 a. $y$ = 720 - 48$x$ b. $y$ = 48$x$ - 720 c. $y$ = $\frac{720}{x}$ - 48 d. $x$ = 720 - 48$y$

Solution:

The total amount collected from the class = $720 The amount charged by caterers =$48 per person

Number of persons attended = x

Total amount charged by the caterers = 48x
[Amount charged = Charge per person × number of persons.]

The balance amount = 720 - 48x
[Balance = Total - amount spent.]

y = 720 - 48x

12.
Which function has an output of $y$ = 0 for an input of $x$ = - 2?
 a. $y$ = 5$x$ b. $y$ = 3$x$ - 1 c. $y$ = 2($x$ - 3) d. $y$ = 5$x$ + 10

Solution:

y = 3x - 1

y = 3(- 2) - 1 = - 7
[Substitute x = - 2.]

y = 2(x - 3)

y = 2(- 2 - 3) = - 10
[Substitute x = - 2.]

y = 5x + 10

y = 5(- 2) + 10 = 0
[Substitute x = - 2.]

So, y = 5x +10 has zero value at x = - 2.

13.
Which of the following rules define $y$ as a function of $x$?

 a. Table-d b. Table-c c. Table-b d. Table-a

Solution:

Since in the Table a, for each value of x there exists a unique value of y. So, Table - a represents a function.

Since in each of the tables b, c, d one value of x corresponds to more than one y-value, these tables do not represent functions.

14.
Which of the following rules define $y$ as a function of $x$?

 a. Table-a b. Table-b c. Table-c d. Table- d

Solution:

Since in each of the choices A,C, D one value of x corresponds to more than one y-value, these tables do not represent functions.

Since in the choice B, each value of x corresponds to a unique value of y, the table represents a function.

15.
Which of the following equations defines $y$ as a function of $x$?
 a. $y$2 = $x$ b. $y$2 = $x$2 c. $y$2 = 8$x$ d. $y$ = 2$x$ + 3

Solution:

Let us discus about each choice.

Consider choice A: y2 = x2

Suppose x = 1, then y2 = 1 y = - 1, 1

Since one value of x can lead to two values of y, y2 = x2 doesnÃ¢â‚¬â„¢t define y as a function of x.

Consider Choice B: y2 = 4x

Suppose x =1, then y2 = 4 y = -2, 2

Since one value of x can lead to two values of y, y2 = 4x doesnÃ¢â‚¬â„¢t define y as a function of x.

Consider Choice C: y2 = 8x

Suppose x =2, then y2 = 16 y = - 4, 4

Since one value of x can lead to two values of y, y2 = 8x doesnÃ¢â‚¬â„¢t define y as a function of x.

Consider Choice D: y = 2x + 3

Since one value of the input variable x can lead to exactly one value of the output Variable, y = 2x + 3 defines y as a function of x.

16.
Which of the following represents a function?

 a. Fig b b. Fig d c. Fig a d. Fig c

Solution:

In the figure a, a vertical line if cuts the graph, cuts in only one point, so this is the graph of a function.

In each of the other three figures b, c, d, it is possible to draw vertical lines which cut the graphs in two points, so these are not the graphs of functions.

17.
Which of the following graphs represents a function?

 a. Fig a b. Fig b c. Fig c d. Fig d

Solution:

In the figures a, b, d, vertical lines are possible to draw which cut the graphs in more than one point, so these graphs do not represent functions.

In the choice C, a vertical line if cuts the graph, cuts in only one point, so this is the graph of a function.

18.
If $f$($x$) = 2$x$2 - 3$x$ + 7, then find the value of $f$(0) + $f$(1).
 a. 6 b. 13 c. 12 d. 7

Solution:

f(x) = 2x2 - 3x + 7

f(0) = 2(0)2 - 3(0) + 7 = 7
[Substitute x = 0 in f(x).]

f(1) = 2(1)2 - 3(1) + 7 = 6
[Substitute x = 1 in f(x).]

So, f (0) + f (1) = 7 + 6 = 13

19.
If $f$($x$) = 3$x$3 - 2$x$2 + $x$ - 3, then find the value of $f$(- 3) - $f$(3).
 a. - 42 b. 42 c. - 168 d. 105

Solution:

f(x) = 3x3 - 2x2 + x - 3

f(- 3) = 3(- 3)3 - 2(- 3)2 + (- 3) - 3 = - 105
[Substitute x = - 3 in f(x).]

f(3) = 3(3)3 - 2(3)2 + 3 - 3 = 63
[Substitute x = 3 in f(x).]

So, f(- 3) - f(3) = - 105 - 63 = - 168

20.
If $f$($x$) = (4$x$ - 5)2, then what is the value of $f$($f$(1)) ?
 a. 9 b. 1 c. 5 d. - 5

Solution:

f(x) = (4x - 5)2

f(1) = (4(1) - 5)2 = 1
[Substitute x = 1 in f(x).]

f(f(1)) = f(1)
[Substitute f(1) = 1.]

= 1
[Substitute f(1) = 1.]