Quiz 1, MAT229

Make sure that your name is on your paper. There are 10 points total. Show work!

1. (3 pts) Given the two points \((2,1)\) and \((5,7)\), write the equation of the line joining them in two ways:
   • Slope-intercept form
   • Point-slope form

2. (4 pts) Draw the graph of the function \[ f(x)=\left\{\begin{array}{cc} {x^2}&{x<-1}\cr {3-x}&{-1 \le x < 1}\cr {\frac{1}{x}}&{x \ge 1} \end{array} \right. \] Make sure to indicate clearly what is happening at the boundaries of the intervals (at \(x=-1\) and at \(x=1\)).

3. (3 pts) We want to shift the graph of the function \(f\) above so that the point at \((1,1)\) is found at \((7,5).\) Find the values of \(a\) and \(b\) such that the appropriate graph is given by that of the function \[ f(x+a)+b \]

4. Extra credit (1 pt): Keith Devlin says that there is "no more beautiful idea in calculus" than what?