The function f(x) = 2^x and g(x) = f(x) + k. if k = 2, what can be determined about the graph of g(x)

We can say that the graph g(x) is obtained by shifting the grapf f(x) by 2 units up.

Step-by-step explanation:

Rule : f(x)→f(x)+k

graph f(x) shifts upward by k units

Since we are given that

So, this means when graph f(x) shifts upward by k units then g(x) is obtained

We are given that k = 2

So, when graph f(x) shifts upward by 2 units then g(x) is obtained .

Thus we can say that the graph g(x) is obtained by shifting the grapf f(x) by 2 units up.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.