Checkpoint: Graphing Reciprocal Functions Solution

Graph the asymptotes and intercepts. Sketch the hyperbola.

$y = \frac{- 1}{x + 3} - 1$

$a = - 1, h = - 3, k = - 1$

$\begin{array}{rcl} 0 & = & \frac{- 1}{x + 3} - 1 \\ 1 & = & \frac{- 1}{x + 3} \\ x + 3 & = & - 1 \\ x & = & - 4 \\ (- 4, 0) \end{array}$

$y = \frac{- 1}{0 + 3} - 1 y = - \frac{4}{3} (0, - \frac{4}{3})$

Note

Q: What happens to the graph when the value of a is negative?
A: It is a reflection as compared to the parent graph.

Q: What parts of the graph should you place on the coordinate plane first when making a graph of a reciprocal function?

A: The asymptotes and intercepts.