03. (a) On a sheel of graph paper, using a scale of 1cm to represent 1 unit on the x-axis and 1cm to
represent 2 units on y-axis, draw the graph of the following straight lines.
(1) Y = 2x + 2
(ii) y - 2x - 3
(iii) y = 2x + 5
(iv) y = 2x -8
(b) What are the gradients of all the four lines?
(c) What do you notice about the lines drawn in part (a)
Answers
Answer:
Equations of the form f(x) = g(x) can be solved graphically by plotting the graphs of y = f(x) and y = g(x). The solution is then given by the x-coordinate of the point where they intersect.
Worked Examples
1
Find any positive solutions of the equation
x2 =
1
x
+ x
by a graphical method.
2
The graph below represents the function
f(x) = x2 − 3x − 3
Use the graph to determine
(a)
the value of f(x) when x = 2
(b)
the value of f(x) when x = −1.5
(c)
the value of x for which f(x) = 0
(d)
the minimum value of f(x)
(e)
the value of x at which f(x) is a minimum
(f)
the solution of x2 − 3x − 3 = 5
(g)
the interval on the domain for which f(x) is less than −3.
3
Given that y = 2x2 − 9x + 4
(a)
copy and complete the table below
x −2 −1 0 2 4 6
y 30 4 0 22
(b)
using a scale of 1 cm to represent 1 unit on the x-axis and 2 cm to represent 5 units on the y-axis, draw the graph of y = 2x2 − 9x + 4 for −2 ≤ x ≤ 6
(c)
use your graph to solve the equation
2x2 − 9x + 4 = 15
4
(a)
The grid on the following page shows the line, l, which passes through the points Q (0, −1) and R (3, 2).
(i)
Determine the gradient of the line, l.
(ii)
Write down the equation of the line, l.
(b)
The table below shows three of the values of f(x) = x2 − 4x + 3 for values of x from 0 to 4.
x 0 1 2 3 4
f(x) 3 −1 0
(i)
Copy the table and insert the missing values of f(x).
(ii)
On a copy of the grid below, draw the graph of f(x) = x2 − 4x + 3.
(iii)
Using the graphs, write down the coordinates of the points of intersection of the line, l, and the graph of f(x).