Question

5. A financial advisor determines that the function f(x) = 5,000(1.08)* models the

value of an investment that earns 8% per year for x years. Identify the domain
and range of the function. Do you think the end behavior of the function
is realistic? Explain.

Answer 1

Part A

The domain is 0 ≤ x ≤ ∞

The range is 5,000 ≤ y ≤ ∞

Part B

The end behavior of the function not realistic

Explanation:

Part A

The given function provided by the financial advisor is presented as follows;

f(x) = 5,000 × 1.08ˣ

The percentage (interest) earned by the investment = 8%

The number of years over which the interest is earned = x

The domain are the possible values of 'x', therefore;

The domain = 0 ≤ x ≤ ∞

The range are the values of the outputs of the function, therefore;

The range = 5,000 ≤ y ≤ ∞

Part B

The end behavior of the function when looking towards the right of the x-axis is not realistic because the investment cannot be expected to produce returns indefinitely.