Answer:
Option (1) is correct.
They will intersect at positive x coordinate.
Step-by-step explanation:
Given : A graph for function f(x)
We have to check weather function f(x) and g(x) intersect or not.
We first determine the function g(x)
Given :
1) x= 1 then g(x) = 5
2) x = 2 then g(x) = 10
Equation of line is given as g(x) = mx + c
Where , m is slope and c is the point where line touches y axis.
Slope [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute,
[tex]m=\frac{10-5}{2-1}=5[/tex]
Substitute we get
y = 5x + c
For c substitute x = 1 y = 5 we get c = 0
Thus g(x) = 5x
Now we plot it on the graph to see whether they intersect or not.
From graph attached below
They will intersect at positive x coordinate.
Option (1) is correct.
