question the graph of $f(x) = -2^x$ is given below. write the equation of a function $g(x)$ which would…
question the graph of $f(x) = -2^x$ is given below. write the equation of a function $g(x)$ which would shift the graph of $f(x)$ left 5 units.
Answer
Explanation:
Step1: Recall horizontal shift rule
For a function ( y = f(x) ), shifting left ( h ) units gives ( y = f(x + h) ).
Step2: Apply shift to ( f(x) = -2^x )
We need to shift left 5 units, so ( h = 5 ). Substitute ( x ) with ( x + 5 ) in ( f(x) ). So ( g(x) = f(x + 5) = -2^{x + 5} ).
Answer:
( g(x) = -2^{x + 5} )