Question

A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. the function f(x) = 100/x -5 represents the remaining time in minutes needed to fill the tank. how is the graph of the parent function f(x) =1/x transformed to create the graph of f(x) = 100/x -5

Answer 1

Answer:

Shifted 5 unit right side then stretched vertically by the factor 100

Step-by-step explanation:

Here, parent function,

$f(x)=\frac{1}{x}$

Transformed function,

$f(x) = \frac{100}{x-5}$

Since, if a function f(x) gives cf(x), where c is any number,

Then the function was vertically stretched by factor c,

While, the function gives f(x-c),

Then the function was shifted c unit right.

Hence, the graph of $f(x)=\frac{1}{x}$ was shifted 5 unit right side then stretched vertically by the factor 100 to create the graph of $f(x)=\frac{100}{x-5}$