Question

The value of a computer that originally sold for $800 can be modeled by g(x)=800(0.8^x), where x is the number of years since the computer was purchased. Describe g(x) as a translation of the parent function f(x)=0.8^x.

Answer 1

Explanation:

The parent function is f(x) = 0.8^x, which represents exponential decay. This means that as x increases, f(x) gets smaller and smaller.

The given function g(x) is obtained by multiplying f(x) by 800, which stretches the graph vertically by a factor of 800.

Also, the function g(x) has an additional translation: the entire graph of f(x) is shifted vertically upwards by 800 units. This is because the computer originally sold for $800, and g(x) represents the current value of the computer, which is $800 times the value of the parent function.

Therefore, g(x) can be described as a vertical stretch and translation of the parent function f(x) = 0.8^x.