The graph which resembles the graph of f(x)=[tex]2^{x}[/tex] but is reflected over the x-axis is g(x)=[tex]2^{x} +1[/tex]
Given Function f(x)=[tex]2^{x}[/tex].
We have to generate a function whose graph is similiar to the given function and is reflected over the x axis.
If we take first function g(x)=2x-1
put the value of x=-1 then the value of function g(x)=2*(-1)-1=-2-1=-3 means the value of y in this function will be negative means the graph will be under x-axis.
Taking second function g(x)=[tex]2^{x} +1[/tex]
for all the negative values of x it posses a positive value of y so the graph will be over the x axis.
Taking third function g(x)=-[tex]2^{x}[/tex]
In the above function for each value of x the function possess a negative value so the graph will be under x axis.
Taking fourth function g(x)=2x-1
For all values of x less than 1 the function becomes negative which takes graph below the x axis. First graph is for [tex]2^{x}[/tex] and the second is for [tex]2^{x} +1[/tex]
Hence the graph similar to [tex]2^{x}[/tex] and reflected over x axis is g(x)=[tex]2^{x} +1[/tex].
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