Question

1: Sketch this function and identify domain, all intercept and the equations of the asymptote
f(x)= 4x+5/x+3

2:An investment of $1,500 averages an interest rate of 4.2% when invested in a government saving bond. If the interest is compounded continuously, how long will it take for the investment to grow to $4,000?

Answer 1

1. The gien function is:

Since, the bove function is not defined when x+3 = 0, i.e. x = -3, so the domain of the above function is the set of all real numbers except at x = -3. So, domain is:

The vertical asymptote is at x = -3 and horizontal asymptote is y = 1.

The x-intercept is given by 4 x + 5 = 0 i.e. at x = - 1.25, so it is (-1.25, 0)

and y intercept is (0, 4/3)

The graph of the function is shown below:

2. Here, the rate of interest r = 0.042. Let t be the time required to reach at desired amount then we have