Question
(a) \( f(x)=\frac{1}{x} \), reflect in the \( x \) axis, shift up by 3
Ask by Riley West. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The transformed function is \( y = -\frac{1}{x} + 3 \).
Solution
Starting with f(x) = 1/x:
1. Reflecting in the x-axis changes the sign of f(x), so it becomes –1/x.
2. Shifting the graph upward by 3 adds 3 to the function, resulting in –1/x + 3.
Thus, the transformed function is y = –1/x + 3.
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Simplify this solution Bonus Knowledge
When you reflect the function \( f(x) = \frac{1}{x} \) in the \( x \)-axis, you get \( f(x) = -\frac{1}{x} \). This transformation flips the graph upside down, turning positive values negative and vice versa. Next, when you shift this reflected function up by 3 units, you add 3 to the entire function, resulting in \( g(x) = -\frac{1}{x} + 3 \). This moves all the points of the graph up, creating a new function that maintains the shape of the original while adjusting its position on the Cartesian plane!
