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The height of water in a bathtub, \(w\), is a function of time, \(t\). Let \(P\) represent this function. Height is measured in inches and time in minutes.
Match each statement in function notation with a description.
\(P(0)=0\)
\(P(4)=10\)
\(P(10)=4\)
\(P(20)=0\)
After 20 minutes, the bathtub is empty.
The bathtub starts out with no water.
After 10 minutes, the height of the water is 4 inches.
The height of the water is 10 inches after 4 minutes.
Function \(C\) takes time for its input and gives a particular student’s Monday class for its output.
Function \(f\) gives the distance of a dog from a post, in feet, as a function of time, in seconds, since its owner left.
Find the value of \(f(20)\) and of \(f(140)\).
Function \(C\) gives the cost, in dollars, of buying \(n\) apples. What does each expression or equation represent in this situation?
A number of identical cups are stacked up. The number of cups in a stack and the height of the stack in centimeters are related.
The number of cups in a stack is a function of the height of the stack in centimeters.
Solve each system of equations without graphing. Explain or show your reasoning.
\(\begin{cases} \text-5x+3y=\text-8 \\ \hspace{1.5mm}3x-7y=\text-3 \\ \end{cases}\)
\(\begin{cases} \text-8x-2y=24 \\ \hspace{1.5mm}5x-3y=\hspace{2.5mm}2 \\ \end{cases}\)