Answer with explanation:
When a graph gets reflected over y-axis it means that a horizontal reflection reflects a graph horizontally over the y-axis.
The graph of [tex]f(x) = 2^x[/tex] is shown on the grid.
The graph of [tex]g(x) = (\dfrac{1}{2})^x[/tex] is the graph of f(x) reflected over the y-axis.
For x= 0 , [tex]g(x) = (\dfrac{1}{2})^0=1[/tex]
For x= 1 , [tex]g(x) = (\dfrac{1}{2})^1=\dfrac{1}{2}=0.5[/tex]
For x= 2 , [tex]g(x) = (\dfrac{1}{2})^2=\dfrac{1}{4}=0.25[/tex]
i.e. graph of g(x) passes through (-1,2) , (0,1) , (1,0.5) , (2,0.25)
From all the given graph , the correct graph is shown below .
It is showing the exact mirror-image of the given graph across y-axis and it is passing through the(-1,2) , (0,1) , (1,0.5) , (2,0.25) .
