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

Answer:

D is correct graph.

Step-by-step explanation:

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

$f(x)=\dfrac{100}{x}$

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

$f(x)=\dfrac{100}{x+20}$

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

$0=\dfrac{100}{x+20}$

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.