$$\text { How can the graph of } f ( x ) = \frac { 1 } { ( x - 10 ) ^ { 2 } } + 4 \text { be obtained from the graph of } y = \frac { 1 } { x ^ { 2 } } \text { ? }$$
A) By making a horizontal shift of 10 units to the right and a vertical shift of 4 units up
B) By making a horizontal shift of 4 units to the right and a vertical shift of 10 units down
C) By making a horizontal shift of 4 units to the left and a vertical shift of 10 units up
D) By making a horizontal shift of 10 units to the left and a vertical shift of 4 units down

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{1}{(x - 10)^2} + 4$ can be derived from $y = \frac{1}{x^2}$ by shifting the graph 10 units to the right (to account for $x - 10$ in the denominator) and then shifting it 4 units up (to account for the "+ 4" outside the fraction).

A) by Making a Horizontal Shift of 10 Units to x