Checkpoint: Reciprocal Functions Solution

Name any asymptotes and intercepts from the equation. Describe the transformation from the parent graph.

$f (x) = \frac{1}{x + 5} - 4$

$a = 1, h = - 5, k = - 4 Asymptotes : x = - 5 y = - 4$

Intercepts:

$\begin{array}{rcl} 0 & = & \frac{1}{x + 5} - 4 \\ 4 & = & \frac{1}{x + 5} \\ 4 (x + 5) & = & 1 \\ 4 x + 20 & = & 1 \\ 4 x & = & - 19 \\ x & = & - \frac{19}{4} \\ (- 4.75, 0) \end{array}$

$f (0) = \frac{1}{0 + 5} - 4 f (0) = - 3 \frac{4}{5} (0, - 3.8)$

The function shifts left 5 spaces and down 4 spaces from the parent graph because $h = - 5, k = - 4$ , and a = 1.

Note

You may write the intercepts as fraction or decimal values. You may feel more comfortable with a decimal value when you graph intercepts. You will plot intercepts and sketch graphs later in this lesson and level.  

Q: What are the values of a, h, and k?

A: a = 1, h = –5, k = –4.  

Q: Why is it not possible for x to equal 5?

A: Because this will make the fraction undefined (or, this makes the denominator zero).