Question

The function f(x) and g(x) are graphed below. If g(x)=f(x+k) what is the value of k?

Answer 1

The graph of g(x) is a horizontal shift to the left of the graph of f(x). Therefore, k must be negative. Since the graph of g(x) is shifted 2 units to the left, k = -2.

Let f(x) be the function represented by the blue graph, and let g(x) be the function represented by the green graph. Then the given information can be expressed as the equation g(x)=f(x+k).

If h is a real number, then the graph of f(x+h) is the graph of f(x) shifted h units to the left. (If h is positive, the graph is shifted h units to the right.) Thus, the graph of g(x)=f(x+k) is the graph of f(x) shifted k units to the left.

From the graph, we see that the graph of g(x) is shifted 2 units to the left of the graph of f(x). Therefore, k= −2

Answer 2

The value of k = -6

Explanation:

First lets concentrate at the most obvious point, the top. Top(f) = ( 4, 1) and Top(g) = ( -2, 1).

The translation factor k ( which is called a vector ), which accounts for the trandlation of any point of f(x) --> g(x).

To translate the x coordinate of the top from 4 to -2, you have to subtract 6 of it.

Because 4 -6 = -2

Hence the factor k must be -6.

The value of k = -6