The function f(x) and g(x) are graphed below.

if g(x)= f(x+k),what is the value of k?

The value of k is:

k=6

Step-by-step explanation:

We are given a graph of the function f(x) and g(x) such that both the graphs are parabola and the graph of g(x) is a shift of graph of f(x) some units to the left.

The vertex of the graph of f(x) is at x=4

whereas the vertex of the graph of the function g(x) is at x= -2.

This means that the graph of g(x) is a shift of the graph of f(x) 6 units to the left.

This means that:

g(x)=f(x+6)

( Since the translation of a function f(x) k units either to the left or to the right is denoted by:

f(x+k)

when k>0 the shift is to the left and if k<0 the shift is to the right.)

This means that the value of k is 6

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents