Which statement best describes the effect of replacing the function f(x) = 2x − 2 with the function g(x) = 2x + 5?
the graph shifts 7 units left.
the graph shifts 5 units left.
the graph shifts 2 units up.
the graph shifts 3 units up.

The  statement which best describes the effect of replacing the function f(x) with g(x) is:

               The graph shifts 7 units up.

The function f(x) is given by :

The function f(x) is a linear function with positive slope.

and the function g(x) is given by:

The function g(x) is a linear function with same positive slope.

Also, we know that any transformation of the type:

f(x) → f(x)+k

is a translation transformation such that it if k>0 then it is a shift k units upwards and if k<0 then it is a shift k units downward.

Here we have:

g(x)=2x+5-2+2

i.e.

g(x)=2x-2+7

i.e.

g(x)=f(x)+7

Hence, the function g(x) is a translation of the function f(x) 7 units upward.

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.