Given:
The graph of the function f is given and the function g is as:
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]
Required:
To graph the function g.
Explanation:
The graph of the function f(x+2), shift the graph f(x) left 2 units by subtracting 2 from the x-coordinates of the points on the graph of f.
The graph of the function
[tex]\frac{1}{2}f(x+2)[/tex]
here
[tex]a=\frac{1}{2}[/tex]
So the graph of g has undergone a vertical shrinking by a factor of
[tex]\frac{1}{2}[/tex]
The graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]
reflect the graph of
[tex]\frac{1}{2}f(x+2)[/tex]
across the x-axis by multiplying the y coordinate of the points on the graph of
[tex]\frac{1}{2}f(x+2)[/tex]
by -1.
Thus the graph of the function
[tex]g(x)=-\frac{1}{2}f(x+2)[/tex]
is as:
Final Answer:
The graph of the function g is attached in the explanation part.
