Applications of Linear Functions

1. (a)  Write a linear function \( f \) that satisfies \( f(-1)= 2\) and \(f(7)=-2 \).  solution

    (b) Write a linear function \( f \) statisfies \(f(2)=5\) and \(f(0)=1\).  solution

2. A ballpen company has a total cost per day consisting of fixed overhead of costs of \( \$4000 \) plus product costs of \(\$.1\) per pen.  Write an equation that can be used to represent the total cost \(C(x)\). Calculate the cost of producing 25,000 pens.  solution

3. If  \(g(x)=\begin{cases} 2x+5,    x < 1\\ 4-2x,  x \geq 1.    \end{cases} \) Find the following: solution

 (a) \( g(0) \)           (b) \(g(-1)\)                 (c) \( g(5) \)

 (d)  sketch the graph of \(y=g(x)\) 

 (e)  the domain and range of \(g\) from the graph.

4. Suppose the tax liability \(T \) on \(x\) dollars of taxable income is given by

\(T(x)=\begin{cases}
0.06x \qquad \qquad \quad \text{if}  \, 0 < x < 30,000,\\
1,800+0.04x \qquad \text{if}  \,  30,000 \leq x < 80,000,\\
5,000+0.05x \qquad \text{if} \, x \geq 80,000.
\end{cases}\)  

Find the tax liability on each taxable income.   solution

(a) \(\displaystyle{\$25,000}\)            (b) \(\displaystyle{\$125,000}\)            (c) \(\displaystyle{\$60,000}\)       

5. Write an equation of the line below.   solution

6. Write a piecewise function for the given graph.  solution