Question

Use the drawing tool(s) to form the correct answer on the provided graph.The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.g(x) = -1/2f(x + 2)

Answer 1

Given:

The graph of the function f is given and the function g is as:

$g(x)=-\frac{1}{2}f(x+2)$

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

$\frac{1}{2}f(x+2)$

here

$a=\frac{1}{2}$

So the graph of g has undergone a vertical shrinking by a factor of

$\frac{1}{2}$

The graph of the function

$g(x)=-\frac{1}{2}f(x+2)$

reflect the graph of

$\frac{1}{2}f(x+2)$

across the x-axis by multiplying the y coordinate of the points on the graph of

$\frac{1}{2}f(x+2)$

by -1.

Thus the graph of the function

$g(x)=-\frac{1}{2}f(x+2)$

is as:

Final Answer:

The graph of the function g is attached in the explanation part.