$$\text { How can the graph of } f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6 \text { be obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ?$$
A) By making a horizontal shift of 1 unit to the right and a vertical shift of 6 units up
B) By reflecting across the x-axis and making a vertical shift of 6 units down
C) By making a horizontal shift of 6 units to the left and a vertical shift of 1 unit down
D) By reflecting across the y-axis and making a horizontal shift of 6 units to the left

Question

Quizplus · Accepted Answer

The graph of $f(x) = -\frac{1}{x^2} - 6$ can be obtained from $y = \frac{1}{x^2}$ by first reflecting it across the x-axis (which changes the sign of the function, making it negative) and then shifting it 6 units down (which is achieved by subtracting 6 from the function).

How can the graph of f(x)=−1x2−6 be obtained from the graph of y=1x2?\text { How can the graph of } f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6 \text { be obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ? How can the graph of f(x)=−x21​−6 be obtained from the graph of y=x21​?

$\text { How can the graph of } f ( x ) = - \frac { 1 } { x ^ { 2 } } - 6 \text { be obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } ?$