the function g(x)=2^x.the function f(x)=2^x+k<0

Question

how is it shifted is it to the left or right

Answer 1

You have two functions.

g(x) = 2^x

f(x) = 2^x+k, such that k < 0

In functions, we observe two forms of shifting. Vertical shift, where we add our number directly to the equation, and horizontal shifting, where we add a number to x. In this equation, we add a number to x in f(x), so we see horizontal shifting.

If we add a positive number to x, we shift left. If we add a negative number to x, we shift right. This is because the number offsets x by it's value. To get x back to the origin (where x = 0), we'll need to reach the opposite of the value added to x. If y = x + 3, then it shifts 3 points to the left since x will have to be -3 to reach the origin (x = 0).

Back to the equation, since k < 0, then k must be a negative number. If k is a negative number, then we know we shift right, since in the equation y = x - |k| must have x equal to +|k| in order to reach the origin.