Question

The table below represents an exponential function, g, that has been vertically shifted from the parent function, f(x) = 2x.

x 0 1 2 3 4
g(x) -11 -10 -8 -4 4

Answer 1

The table shows that the function g(x) has been shifted 11 units downward from the parent function f(x). This is because the values of g(x) are 11 less than the corresponding values of f(x). For example, g(0) = -11 and f(0) = 1, so g(x) is 11 units below f(x) when x = 0.

We can write the equation for g(x) as follows:

g(x) = f(x) - 11 = 2x - 11

This equation shows that the function g(x) is a vertical shift of the function f(x) by 11 units downward.