# 12 Basic Functions Worksheet

12 Basic Functions Worksheet
• Page 1
1.
Select the graph of the function $y$ = 1 - sin $x$.

 a. Graph A b. Graph B c. Graph C d. None of the above

#### Solution:

y = 1 - sin x

The graph of the function y = 1 - sin x is obtained by shifting the graph of the function y = - sin x, one unit up.

Hence, Graph A represents the graph of the function y = 1 - sin x.

2.
Find the minimum value of the function $y$ = ($x$ - 7)2.
 a. -7 b. 7 c. 1

#### Solution:

y = (x - 7)2

(x - 7)2 ≥ 0
[Square term is always non negative.]

So, the minimum value of (x - 7)2 is 0.

3.
Which is the graph of the function $y$ = - 3$x$?

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

#### Solution:

The graph of the function y = - 3x is the reflection of the graph y = 3x about the x-axis.

Hence, Graph 3 is the correct choice.

4.
Select the graph of the function $y$ = |$x$| + 1.

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

#### Solution:

y = |x| + 1

For all x R, y = |x| + 1 is always positive.

Hence, Graph 2 is the correct choice.

5.
Which of the following graphs represents the graph of an even function?

 a. Graph 1 b. Graph 2 c. Graph 3 d. All of the above

#### Solution:

The graph of an even function should be symmetric with respect to y-axis.

From the given graphs, all of them are symmetric with respect to y-axis.

6.
Choose the graph of the function $y$ = |$x$| + 2.

 a. Graph 1 b. Graph 2 c. Graph 3 d. None of the above

#### Solution:

The graph of the function y = |x| + 2 is obtained on shifting the graph of y = |x| by 2 units up.

Hence, Graph 1 is the correct choice.

7.
Choose the graph of the function $y$ = ($x$ - 2)2.

 a. Graph 1 b. Graph 2 c. Graph 3 d. None of the above

#### Solution:

The graph of the function y = (x - 2)2 is just the graph of y = x2 moved 2 units to the right.

Hence, Graph 2 is the correct choice.

8.
Which of the following graphs of basic functions are bounded both above and below?

 a. Graph 1 b. Graph 2 c. Graph 3 d. None of the above

#### Solution:

A function that is bounded must have a graph that lies entirely between two horizontal lines.
[Definition for boundedness.]

For Graph 1:
The graph of the function has two horizontal asymptotes, the x-axis and the line y = 1. The graph lies entirely between y = 0 and y = 1. Hence, it is bounded.

For Graph 2:
The graph of the function y = 1x has one horizontal asymptote, x = 0 and one vertical asymptote, y = 0. Hence, it is not bounded.

For Graph 3:
The graph of y = x3 extends with no horizontal boundaries. Hence, it is unbounded.

9.
Which of the following graphs represents an identity function?

 a. Graph A b. Graph B c. Graph C d. None of the above

#### Solution:

The mapping f : A A defined by f (x) = x or the mapping from A to A such that every element of A is f image of itself is called Identity function on A.
[Definition of Identity function.]

From the given graphs, Graph B represents the identity function f (x) = x.

10.
Select the graph of the function $y$ = - cos $x$.

 a. Graph A b. Graph B c. Graph C d. None of the above

#### Solution:

The graph of the function y = - cos x is the reflection of the graph of y = cos x about the x-axis.

Hence, Graph B represents the graph of the function y = - cos x.