Question

how does the graph of (g(x) = \frac{1}{x+4} - 6) compare to the graph of the parent function (f(x) = \frac{1}{x})?

(g(x)) is shifted 4 units right and 6 units up from (f(x)).
(g(x)) is shifted 4 units right and 6 units down from (f(x)).
(g(x)) is shifted 4 units left and 6 units up from (f(x)).
(g(x)) is shifted 4 units left and 6 units down from (f(x)).

Explanation:

Identify the transformation parameters

Using the Rational Function Transformations and Parent Function Comparison knowledge points

$$
LATEXBLOCK0
$$

Determine the horizontal shift

Using the Rational Function Transformations knowledge point

$$
LATEXBLOCK1
$$

Determine the vertical shift

Using the Rational Function Transformations knowledge point

$$
LATEXBLOCK2
$$

Answer:

• g(x) is shifted 4 units right and 6 units up from f(x).
• g(x) is shifted 4 units right and 6 units down from f(x).
• g(x) is shifted 4 units left and 6 units up from f(x).
• g(x) is shifted 4 units left and 6 units down from f(x). (Correct answer)