an employee at a garden center fills a water tank once a day around noon to a height of 20 inches. the…

an employee at a garden center fills a water tank once a day around noon to a height of 20 inches. the function m models the height of the water in the tank, m(x), in inches, x seconds after 12:00 p.m. on monday as it fills. the function t gives the height of the water in the tank, t(x), in inches, x seconds after 12:00 p.m. on tuesday as it fills. here are the graphs of m and t. a. write a function t(x) in terms of m(x).

an employee at a garden center fills a water tank once a day around noon to a height of 20 inches. the function m models the height of the water in the tank, m(x), in inches, x seconds after 12:00 p.m. on monday as it fills. the function t gives the height of the water in the tank, t(x), in inches, x seconds after 12:00 p.m. on tuesday as it fills. here are the graphs of m and t. a. write a function t(x) in terms of m(x).

Answer

Explanation:

Step1: Observe the graphs

The graph of $T(x)$ is a horizontal - shift of the graph of $M(x)$. The graph of $T(x)$ starts later than the graph of $M(x)$.

Step2: Determine the shift

The graph of $M(x)$ starts at $x = 0$, and the graph of $T(x)$ starts at approximately $x = 10$. This means that the function $T(x)$ is a horizontal shift of $M(x)$ to the right by 10 units. The rule for a horizontal shift of a function $y = f(x)$ to the right by $h$ units is $y=f(x - h)$. Here, $h = 10$ and $f(x)=M(x)$. So, $T(x)=M(x - 10)$.

Answer:

$T(x)=M(x - 10)$