A function, f(x)=1x+4

Question

𝑓
(
𝑥
)
=
1
𝑥
+
4
, is reflected. Its image is the function g(x)=−1x−4
𝑔
(
𝑥
)
=
−
1
𝑥
−
4
. Select the rule used to reflect the function.(1 point)
Responses

ry−axis
𝑟
𝑦
−
𝑎
𝑥
𝑖
𝑠
r subscript y axis baseline

ry=4
𝑟
𝑦
=
4
r subscript y equals 4 baseline

ry=−4
𝑟
𝑦
=
−
4
r subscript y equals negative 4 baseline

rx−axis

Answer 1

To determine the rule used to reflect the function \( f(x) = \frac{1}{x} + 4 \) to get \( g(x) = -\frac{1}{x} - 4 \), we should look at the transformations involved.

1. Reflection over the \( x \)-axis would change the sign of the entire function. In this case, \( f(x) \) changes to \( -f(x) \).
2. The term \( +4 \) in the function \( f(x) \) is a vertical shift upward. The reflection over the \( x \)-axis will also affect this constant term, making it \( -4 \) instead of \( +4 \).

The transformation from \( f(x) = \frac{1}{x} + 4 \) to \( g(x) = -\frac{1}{x} - 4 \) indicates that the reflection is with respect to the \( x \)-axis.

Therefore, the correct response is:

rx−axis