13.2.3 Graphs of Functions, PT3 Focus Practice


Question 7:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.


The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 5 units, complete and label the y-axis.
(b) Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.

Answer:


Solution:



Question 8:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.


The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 2 units, complete and label the y-axis.
(b) Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.

Answer:


Solution:


13.2.2 Graphs of Functions, PT3 Focus Practice


13.2.2 Graphs of Functions, PT3 Focus Practice

Question 4:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.

x
–3
–2
–1
0
1
2
3
y
–19
–3
1
–1
–3
1
17
The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 5 units, complete and label the y-axis.
(b) Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.

Answer:



Solution:





Question 5:
Use graph paper to answer this question.
Table below shows the values of two variables, x and y, of a function.

x
–4
–3
–2
–1
0
1
2
y
31
17
7
1
–1
1
7
The x-axis and the y-axis are provided on the graph paper on the answer space.
(a) By using a scale of 2 cm to 5 units, complete and label the y-axis.
(b)   Based on the table above, plot the points on the graph paper.
(c) Hence, draw the graph of the function.


Answer:



Solution:







Question 6:
(a) Complete table below in the answer space for the equation L = x2 + 5x by writing the value of L when x = 2.
(b) Use graph paper to answer this part of the question. You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of L = x2 + 5x for 0 ≤ x ≤ 4.

Answer:


Solution:
(a)
When x = 2
L = 22 + 5(2)
= 4 + 10
= 14  

(b)



13.2.1 Graphs of Functions, PT3 Focus Practice


13.2.1 Graphs of Functions, PT3 Focus Practice
 
Question 1:
 
In the figure shown, when x = 4, the value of y is

Solution:
 
is the point on the graph where x = 4.
Hence, when x = 4, y = 5.


Question 2:
Diagram shows the graph of a function on a Cartesian plane.
 
The equation that represents the function is
 
Solution:
Use points (0, 6) and (-3, 0) to determine the function.

Function
Value of y when
x = 0
x = –3
y = x + 3
3
0
y = x – 3
–3
–6
y = 2x + 6
6
0 (correct)
y = 2x – 6
–6
–12

Question 3:
Table below shows the values of variables x and y of a function.
 
x
–2
0
1
y
–6
2
3
Which of the following functions is satisfied by the ordered pair?
A = 7x + 2
B = x3 + 2
C = x + x2 – 2
D = x2 + 2

Solution:
Only y = x3 + 2 is satisfied by all the ordered pairs.
(i) –6 = (–2)3 + 2
(ii)   2 = 03 + 2
(iii)  3 = 13 + 2
Answer = B

13.1 Graphs of Functions


13.1 Graphs of Functions
 
13.1.1 Functions
1.   Function is a relationship that expresses a variable (dependent) in terms of another variable (independent).
 
  

2.   is a function of x if and only if every value of x corresponds to only one value of y.


13.1.2  Graphs of Functions
1.   A graph of function is a representation of the function as one or more lines on a coordinate plane.
Example:

2.  
When drawing graphs of functions, it is best to observe these few points:
· choose suitable scales for both axes.
· use at least three points to draw a straight line to ensure accuracy.
· use at least five points to draw a curve to ensure accuracy.