Which of the following graphs represents the function f(x) = x3- x2-10x-8?
Solution:
It is given that
f(x) = x3- x2 - 10x - 8
Let us find the point when x = 0
In f(x) replace x by 0
f(0) = 03- 02 - 10 (0) - 8 = -8
Let us find the point when x = 1
In f(x) replace x by 1
f(1) = 13- 12 - 10 (1) - 8
f(1) = 1 - 1 - 10 - 8
f(1) = -18
Let us find the point when x = -1
In f(x) replace x by -1
f(-1) = (-1)3- (-1)2 - 10 (-1) - 8
f(-1) = -1 - 1 + 10 - 8
f(-1) = 0
Let us find the point when x = 3
In f(x) replace x by 3
f(3) = (3)3- (3)2 - 10 (3) - 8
f(3) = 27 - 9 - 30 - 8
f(3) = -20
Let us find the point when x = -2
In f(x) replace x by -2
f(-2) = (-2)3- (-2)2 - 10 (-2) - 8
f(-2) = -8 - 4 + 20 - 8
f(-2) = 0
Let us find the point when x = 2
In f(x) replace x by 2
f(2) = (2)3- (2)2 - 10 (2) - 8
f(2) = 8 - 4 - 20 - 8
f(2) = -24
Let us find the point when x = 5
In f(x) replace x by 5
f(5) = (5)3- (5)2 - 10 (5) - 8
f(5) = 125 - 25 - 50 - 8
f(5) = 42
Now we can plot a graph using the following points
|
x |
0 |
1 |
-1 |
3 |
-2 |
2 |
5 |
|
y |
-8 |
-18 |
0 |
-20 |
0 |
-24 |
42 |
Therefore, the above mentioned graph represents the function f(x) = x3 - x2 -10x - 8.
Which of the following graphs represents the function f(x) = x3- x2-10x-8?
Summary:
The graph mentioned above function f(x) = x3- x2-10x-8. We have drawn graph by plotting x and corresponding y values.