Question

Describe how the graph of

g(x) = 4(0.5)x - 3
compares to the graph of
f(x) = 4(0.5)x .

Answer 1

the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.

Explanation:

The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.

However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.

In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.