[size=150]Let [math]C[/math] represent Noah's cousin's age and [math]N[/math]represent Noah's age. Ages are measured in years.[/size][br][br]Write a function that defines the cousin's age as a function of Noah's age. What are the input and output of this function?

Write the inverse of the function you wrote. What are the input and output of this inverse function?[br]

[size=150]Let [math]M[/math] represent Noah's cousin's age in months and [math]N[/math] represent Noah's age in years.[/size][br][size=100][br]If Noah is 15 years old, how old is his cousin, in months?[/size]

When Noah's cousin is 132 months old, how old is Noah, in years?[br]

Write a function that gives the age of Noah's cousin in months, as a function of Noah's age in years.[br]

Write the inverse of the function you wrote. What are the input and the output of this inverse function?[br]

[math]c=w+3[/math]

[math]y=x-2[/math]

[math]y=5x[/math]

[math]w=\frac{d}{7}[/math]

[size=150]The number of years, [math]y[/math], is a function of the number of months, [math]m[/math]. The number of months, [math]m[/math], is also a function of the number of years, [math]y[/math]. [/size][br][br]Write two equations, one to represent each function.

Explain why the two functions are inverses.  [br]

Which of the following inputs is impossible for this function?

[math]\displaystyle f(x)=\begin{cases} 7,& 8\leq x\leq 12 \\ 8, & 12< x\leq 13 \\ 9, & 13< x\leq 14\\ 10, & 14< x\leq 15\\ 11, & 15< x\leq 16\\ \end{cases}[/math][br][br]Describe the instructions in words so that they can be followed by someone using the pressure cooker.

[size=150]The absolute value function [math]Q\left(x\right)=|x|[/math] gives the distance from 0 of the point [math]x[/math] on the number line.[br][math]Q[/math] can also be defined using piecewise notation: [/size][br][math]Q(x)=\begin{cases} x,& x\geq 0 \\ \text-x,& x < 0 \end{cases}[/math][br][br]Determine if the point [math](-3,3)[/math] is on the graph of [math]Q[/math]. [br]For each point that you believe is [i]not[/i] on the graph of [math]Q[/math], change the output coordinate so that the point is on the graph of [math]Q[/math].

Determine if point [math](0,0)[/math] is on the graph of [math]Q[/math]. [br]For each point that you believe is [i]not[/i] on the graph of [math]Q[/math], change the output coordinate so that the point is on the graph of [math]Q[/math].

Determine if point [math](-5,-5)[/math] is on the graph of [math]Q[/math]. [br]For each point that you believe is [i]not[/i] on the graph of [math]Q[/math], change the output coordinate so that the point is on the graph of [math]Q[/math].

Determine if point [math](-72,72)[/math] is on the graph of [math]Q[/math]. [br]For each point that you believe is [i]not[/i] on the graph of [math]Q[/math], change the output coordinate so that the point is on the graph of [math]Q[/math].

Determine if point [math]\left(\frac{4}{5},\text{-}\frac{4}{5}\right)[/math] is on the graph of [math]Q[/math]. [br]For each point that you believe is [i]not[/i] on the graph of [math]Q[/math], change the output coordinate so that the point is on the graph of [math]Q[/math].