Answer:
A = (-1, 0)
B = (0, -1)
C = (0, -2)
Explanation:
Coordinates of A
To determine the coordinates of A set any of the equations to zero.
[tex]\sf \rightarrow -\dfrac{2}{x} -2 = 0[/tex]
[tex]\sf \rightarrow -\dfrac{2}{x} = 2[/tex]
[tex]\sf \rightarrow -2 = 2x[/tex]
[tex]\sf \rightarrow x = -1[/tex]
As the point lies on the x axis, y = 0.
So A coordinates: (-1, 0)
Coordinates of B
To find the coordinates of B set x = 0 in the equation f(x) = (1/2)^x - 2
[tex]\sf \rightarrow y = (\dfrac{1}{2} )^x - 2[/tex]
[tex]\sf \rightarrow y = (\dfrac{1}{2} )^0 - 2[/tex]
[tex]\sf \rightarrow y = 1 - 2[/tex]
[tex]\sf \rightarrow y = -1[/tex]
As the point lies on the y axis, x = 0.
So B coordinates: (0, -1)
Coordinates of C
To find the coordinates of C insert any high limit value in both eq.
[tex]\sf \rightarrow y = (\dfrac{1}{2} )^{10000} - 2=-2[/tex]
[tex]\sf \rightarrow y = -\dfrac{2}{10000} -2 = -2.0002[/tex]
So estimated that y = -2 and x = 0 as lies on y axis.
So C coordinates: (0, -2)
