Question

A 100-gallon fish tank fills at a rate of x gallons per minute. The function is F(x)=100/x. if the tank has been filling for 20 minutes, the total time to fill the tank is represented by the function f(x)=100/x+20. Which graph represents this

Answer 1

The second graph is correct.

There will be a vertical asymptote at x=0, since we cannot divide by 0. Using the x-axis on the second graph, if we substitute 5 in for x, we have 100/5+20 = 20+20=40. There is a point on this graph here. Using 10 for x, we have 100/10+20 = 10+20 = 30. There is a point on the graph here. Every point matches.

Answer 2

D is correct graph.

Explanation:

A 100-gallon fish tank fills at a rate of x gallons per minute.

`f(x)=(100)/(x)`

If the tank has filling for 20 minutes, The total time to fill the tank is represented by the function,

`f(x)=(100)/(x+20)`

It is rational function. We need to draw the graph of this function.

First we find vertical asymptote.

For VA: x+20=0

x=-20

For x-intercept, Put f(x)=0

`0=(100)/(x+20)`

No x-intercept

For y-intercept, Put x=0

y-intercept: (0,5)

For HA,
`x\rightarrow \infty`

y=0

Please see the attachment for graph.

Hence, D is correct graph.