The graph of function f is shown on the coordinate plane. Graph the line representing function g, if g is defined as shown below.

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Question:

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)

Step-by-step explanation:

Any problem of this kind should first be approached by solving the initial function.

This question is based on curve translation on x-axis. But, there can be questions asked on translation in both axes, rotation of curve about origin, or both combined.

Initial function f(x) is a straight line from picture.

Common equation of straight line is

m= slope of the line

c= y-intercept

Slope of the line:

Let those points on graph be A(3,0) and B(0,-6)

Therefore, slope of line AB, using formula is:

m=2

And c=(-6)

And equation of line AB is:

Now this line is translated backwards by 2 units, (x) becomes (x+2)

Let us consider a X, such that,

Now, there is another function such that,