The difference between the functions f(x) and g(x) is the addition of a
constant to the value of x and changing
the sign of the output.
The graph of g(x) compared to f(x) is g(x) is shifted 3 units to the left and
reflected over the x-axis.
Reason:
The addition of a positive constant term to the input variable of a function,
shifts the graph to the left of the graph of
the parent function.
Please find attached the image of the graph of f(x), which is g(x) shifted to
the left by 3 units.
Step-by-step explanation:
Changing the sign of the output value from positive to negative;
When the output value of a function is changed from positive to negative,
and vice versa, it is equivalent to a reflection across the x-axis.
Therefore, the function g(x) is a reflection across the x-axis.
Therefore;
g(x) is shifted 3 units to the left and
reflected over the x-axis.
