How can the graph of $f ( x ) = - \frac { 1 } { x } - 4$ be obtained from the graph of $y = \frac { 1 } { x }$ ?
A) By making a horizontal shift of 4 units to the left and a vertical shift of 1 unit down
B) By reflecting across the $x$-axis and making a vertical shift of 4 units down
C) By reflecting across the $y$-axis and making a horizontal shift of 4 units to the left
D) By making a horizontal shift of 1 unit to the right and a vertical shift of 4 units up

Question

Quizplus · Accepted Answer

The graph of $f(x) = -\frac{1}{x} - 4$ can be obtained from $y = \frac{1}{x}$ by first reflecting it across the $x$-axis (to account for the negative sign, making it $-\frac{1}{x}$) and then shifting it 4 units down (to account for the "-4" in the equation).

How Can the Graph Of f(x)=−1x−4f ( x ) = - \frac { 1 } { x } - 4f(x)=−x1​−4

How Can the Graph Of $f ( x ) = - \frac { 1 } { x } - 4$